Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-19T08:45:58.576Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  08 February 2024

Robin Pemantle
Affiliation:
University of Pennsylvania
Mark C. Wilson
Affiliation:
University of Massachusetts, Amherst
Stephen Melczer
Affiliation:
University of Waterloo, Ontario
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2024

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aldous, D. and Bandyopadhyay, A.. “A survey of max-type recursive distributional equations”. Ann. Appl. Prob. 15 (2005), 10471110 (cit. on p. 75).CrossRefGoogle Scholar
Adamczewski, B. and Bell, J. P.. “Diagonalization and rationalization of algebraic Laurent series”. Ann. Sci. Éc. Norm. Supér. (4) 46 (2013), 9631004 (cit. on p. 56).CrossRefGoogle Scholar
Atiyah, M. F., Bott, R., and Gårding, L.. “Lacunas for hyperbolic differential operators with constant coefficients I”. Acta Mathematica 124 (1970), 109189 (cit. on pp. 15, 126, 211, 217, 340, 353, 355, 365, 379, 522).Google Scholar
Andreotti, A. and Frankel, T.. “The Lefschetz theorem on hyperplane sections”. Ann. of Math. (2) 69 (1959), 713717 (cit. on p. 477).Google Scholar
Askey, R. and Gasper, G.. “Certain rational functions whose power series have positive coefficients”. Amer. Math. Monthly 79 (1972), 327341 (cit. on p. 376).Google Scholar
Aldous, D.. “A Metropolis-Type Optimization Algorithm on the Infinite Tree”. Algorithmica 22 (1998), 388412 (cit. on p. 75).Google Scholar
Ambainis, A. et al. “One-dimensional quantum walks”. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing. New York: ACM Press, 2001, 3749 (cit. on p. 286).Google Scholar
André, Y.. G-functions and geometry. Aspects of Mathematics, E13. Friedr. Vieweg & Sohn, Braunschweig, 1989 (cit. on p. 241).Google Scholar
Aĭzenberg, I. A. and Yuzhakov, A. P.. Integral representations and residues in multidimensional complex analysis. Vol. 58. Translations of Mathematical Monographs. Providence, RI: American Mathematical Society, 1983, x+283 (cit. on pp. 9, 328, 337, 489, 490, 511).Google Scholar
Banderier, C. et al. “Random maps, coalescing saddles, singularity analysis, and Airy phenomena”. Random Structures Algorithms 19 (2001), 194246 (cit. on p. 426).Google Scholar
Baryshnikov, Y. et al. “Two-dimensional quantum random walk”. J. Stat. Phys. 142 (2010), 78107 (cit. on pp. 219, 281, 286, 289, 398, 422).CrossRefGoogle Scholar
Baryshnikov, Y. et al. “Diagonal asymptotics for symmetric rational functions via ACSV”. In: 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Vol. 110. Dagstuhl, 2018, 12 (cit. on p. 434).Google Scholar
Barvinok, A.. “A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed.” Math. of Operations Res. 19 (1994), 769779 (cit. on p. 338).Google Scholar
Basu, S.. “Algorithmic semi-algebraic geometry and topology—recent progress and open problems”. In: Surveys on discrete and computational geometry. Vol. 453. Contemp. Math. Amer. Math. Soc., Providence, RI, 2008, 139212 (cit. on p. 468).Google Scholar
Borcea, J. and Brändén, P.. “The Lee-Yang and Pólya-Schur programs, II: Theory of stable polynomials and applications”. Comm. Pure Appl. Math. 62 (2009), 15951631 (cit. on pp. 159, 434).CrossRefGoogle Scholar
Borcea, J., Brändén, P., and Liggett, T.. “Negative dependence and the geometry of polynomials”. J. AMS 22 (2009), 521567 (cit. on p. 379).Google Scholar
Bena, I. et al. “Scaling BPS solutions and pure-Higgs states”. J. High Energy Phys. (2012), 171, front matter + 36 (cit. on p. 289).Google Scholar
Bender, E. A.. “Central and local limit theorems applied to asymptotic enumeration”. J. Combinatorial Theory Ser. A 15 (1973), 91111 (cit. on pp. 8, 386).CrossRefGoogle Scholar
Bender, E. A.. “Asymptotic methods in enumeration”. SIAM Rev. 16 (1974), 485515 (cit. on p. 8).Google Scholar
Bergman, G. M.. “The logarithmic limit-set of an algebraic variety”. Trans. Amer. Math. Soc. 157 (1971), 459469 (cit. on p. 164).Google Scholar
Baouendi, S., Ebenfelt, P., and Rothschild, J.. Real Submanifolds in Complex Space and Their Mappings. Princeton: Princeton University Press, 1999, xi1+404 (cit. on p. 126).CrossRefGoogle Scholar
Berenstein, C. A. and Gay, R.. Complex variables. Vol. 125. Graduate Texts in Mathematics. New York: Springer-Verlag, 1991, xii+650 (cit. on p. 8).Google Scholar
Banderier, C. and Hitczenko, P.. “Enumeration and asymptotics of restricted compositions having the same number of parts”. Discrete Appl. Math. 160 (2012), 25422554 (cit. on p. 423).Google Scholar
Bleistein, N. and Handelsman, R. A.. Asymptotic expansions of integrals. Second edition. New York: Dover Publications Inc., 1986, xvi+425 (cit. on pp. 13, 112, 131).Google Scholar
Bröcker, T. and Jänich, K.. Introduction to Differential Topology. New York: Cambridge University Press, 1982, vii+160 (cit. on p. 272).Google Scholar
Baryshnikov, Y., Jin, K., and Pemantle, R.. “Coefficient asymptotics of algebraic multivariable generating functions”. Preprint (2023), 30 (cit. on pp. 431, 436).Google Scholar
Bostan, A., Lairez, P., and Salvy, B.. “Creative telescoping for rational functions using the Griffiths-Dwork method”. In: ISSAC 2013—Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation. ACM, New York, 2013, 93100 (cit. on p. 241).Google Scholar
Bertozzi, A. and McKenna, J.. “Multidimensional residues, generating functions, and their application to queueing networks”. SIAM Rev. 35 (1993), 239268 (cit. on pp. 10, 310, 337).Google Scholar
Bierstone, E. and Millman, P.. “Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant”. Inventiones Mathematicae 128 (1997), 207302 (cit. on p. 380).Google Scholar
Baryshnikov, Y., Melczer, S., and Pemantle, R.. “Asymptotics of multivariate sequences in the presence of a lacuna”. arXiv preprint arXiv:1905.04174 (2019) (cit. on p. 376).Google Scholar
Baryshnikov, Y., Melczer, S., and Pemantle, R.. “Stationary points at infinity for analytic combinatorics”. Found. Comput. Math. 22 (2022), 16311664 (cit. on pp. 200, 215–217, 219, 234, 235, 289, 530).CrossRefGoogle Scholar
Baryshnikov, Y., Melczer, S., and Pemantle, R.. “Asymptotics of multivariate sequences IV: generating functions with poles on a hyperplane arrangement”. Accepted to Annals of Combinatorics (2023) (cit. on pp. 302, 307, 312, 335, 337).Google Scholar
Bostan, A. et al. “Differential equations for algebraic functions”. In: ISSAC 2007. New York: ACM, 2007, 2532 (cit. on p. 56).Google Scholar
Bousquet-Mélou, M. and Petkovšek, M.. “Linear recurrences with constant coefficients: the multivariate case”. Discrete Math. 225 (2000), 5175 (cit. on pp. 32, 35, 36, 56).Google Scholar
Bressler, A. and Pemantle, R.. “Quantum random walks in one dimension via generating functions”. In: 2007 Conference on Analysis of Algorithms, AofA 07. Discrete Math. Theor. Comput. Sci. Proc., AH. Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2007, 403412 (cit. on pp. 259, 395, 422).Google Scholar
Baryshnikov, Y. and Pemantle, R.. “Asymptotics of multivariate sequences, part III: quadratic points”. Advances in Mathematics 228 (2011), 31273206 (cit. on pp. 15, 212, 219, 289, 340, 341, 352–354, 359, 361, 365, 366, 374, 375, 379, 380, 433, 522).Google Scholar
Baryshnikov, Y. and Pemantle, R.. “Elliptic and hyper-elliptic asymptotics of trivariate generating functions with singularities of degree 3 and 4”. Manuscript in progress (2021) (cit. on p. 212).Google Scholar
Basu, S., Pollack, R., and Roy, M.-F.. Algorithms in real algebraic geometry. Vol. 10. Algorithms and Computation in Mathematics. Springer-Verlag, Berlin, 2003 (cit. on pp. 184, 227, 466).Google Scholar
Bender, E. A. and Richmond, L. B.. “Central and local limit theorems applied to asymptotic enumeration. II. Multivariate generating functions”. J. Combin. Theory Ser. A 34 (1983), 255265 (cit. on pp. xiv, 8, 9, 288, 385, 386).Google Scholar
Bender, E. A. and Richmond, L. B.. “Multivariate asymptotics for products of large powers with applications to Lagrange inversion”. Electron. J. Combin. 6 (1999), Research Paper 8, 21 pp. (electronic) (cit. on pp. 9, 386).Google Scholar
Briand, E.. “Covariants vanishing on totally decomposable forms”. In: Liaison, Schottky problem and invariant theory. Vol. 280. Progr. Math. Basel: Birkhäuser Verlag, 2010, 237256 (cit. on p. 325).Google Scholar
Brieskorn, E.. “Sur les groupes de tresses”. In: Séminaire Boubaki. Vol. 317. Berlin: Springer-Verlag, 1973, 2144 (cit. on p. 478).Google Scholar
Bender, E. A., Richmond, L. B., and Williamson, S. G.. “Central and local limit theorems applied to asymptotic enumeration. III. Matrix recursions”. J. Combin. Theory Ser. A 35 (1983), 263278 (cit. on p. 9).CrossRefGoogle Scholar
Brylawski, T.. “The broken-circuit complex”. Trans. AMS 234 (1977), 417433 (cit. on p. 311).Google Scholar
Buchberger, B.. “Ein Algorithmus zum Auffinden der Basise-lemente des Restklassenringes nach einem nulldimensionalen Polynomideal”. PhD thesis. University of Innsbruck, 1965 (cit. on p. 243).Google Scholar
Bruhat, F. and Whitney, H.. “Quelques propriétés fondamentales des ensembles analytiques-réels”. Comment. Math. Helvetici 33 (1959), 132160 (cit. on p. 126).Google Scholar
Becker, T. and Weispfenning, V.. Gröbner bases. Vol. 141. Graduate Texts in Mathematics. Springer-Verlag, New York, 1993 (cit. on p. 226).CrossRefGoogle Scholar
Chen, W. Y. C., Deutsch, E., and Elizalde, S.. “Old and young leaves on plane trees”. European Journal of Combinatorics 27 (2006), 414427 (cit. on p. 59).Google Scholar
Christol, G.. “Diagonals of rational fractions”. Eur. Math. Soc. Newsl 97 (2015), 3743 (cit. on p. 57).Google Scholar
Carteret, H. A., Ismail, M. E. H., and Richmond, L. B.. “Three routes to the exact asymptotics for the one-dimensional quantum walk”. J. Phys. A 36 (33 2003), 87758795 (cit. on p. 421).Google Scholar
Cox, D., Little, J., and O’Shea, D.. Using algebraic geometry. Second edition. Vol. 185. Graduate Texts in Mathematics. New York: Springer, 2005, xii+572 (cit. on p. 244).Google Scholar
Cox, D., Little, J., and O’Shea, D.. Ideals, varieties, and algorithms. Third edition. Undergraduate Texts in Mathematics. New York: Springer, 2007, xvi+551 (cit. on pp. 222, 224, 233, 243).Google Scholar
Corteel, S., Louchard, G., and Pemantle, R.. “Common intervals of permutations”. In: Mathematics and computer science. III. Trends Math. Basel: Birkhäuser, 2004, 314 (cit. on p. 24).Google Scholar
Canfield, E. R. and McKay, B.. “The asymptotic volume of the Birkhoff polytope”. Online J. Anal. Comb. 4 (2009), 4 (cit. on p. 338).Google Scholar
Comtet, L.. “Calcul pratique des coefficients de Taylor d’une fonction algébrique”. Enseignement Math. (2) 10 (1964), 267270 (cit. on p. 56).Google Scholar
Comtet, L.. Advanced combinatorics. Enlarged edition. Dordrecht: D. Reidel Publishing Co., 1974, xi+343 (cit. on pp. 24, 251, 406).Google Scholar
Conley, C.. Isolated invariant sets and the Morse index. Vol. 38. CBMS Regional Conference Series in Mathematics. Springer-Verlag, 1978 (cit. on p. 204).Google Scholar
Conway, J. B.. Functions of one complex variable. Second edition. Vol. 11. Graduate Texts in Mathematics. New York: Springer-Verlag, 1978, xiii+317 (cit. on pp. 8, 62, 164, 349).Google Scholar
Cox, D.. “Reflections on elimination theory”. In: ISSAC’20—Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation. ACM, New York, 2020, 14 (cit. on p. 244).Google Scholar
Chyzak, F. and Salvy, B.. “Non-commutative elimination in Ore algebras proves multivariate identities”. J. Symbolic Comput. 26 (1998), 187227 (cit. on p. 47).Google Scholar
de Andrade, R. F., Lundberg, E., and Nagle, B.. “Asymptotics of the extremal excedance set statistic”. European J. Combin. 46 (2015), 7588 (cit. on p. xi).Google Scholar
de Bruijn, N. G.. Asymptotic methods in analysis. Third edition. New York: Dover Publications Inc., 1981, xii+200 (cit. on pp. 6, 12, 112).Google Scholar
DeVries, T.. “A case study in bivariate singularity analysis”. In: Algorithmic probability and combinatorics. Vol. 520. Contemp. Math. Providence, RI: Amer. Math. Soc., 2010, 6181 (cit. on pp. 10, 270).Google Scholar
DeVries, T.. “Algorithms for bivariate singularity analysis”. PhD thesis. University of Pennsylvania, 2011 (cit. on pp. 262, 269).Google Scholar
Delabaere, E. and Howls, C. J.. “Global asymptotics for multiple integrals with boundaries”. Duke Math. J. 112 (2002), 199264 (cit. on p. 422).CrossRefGoogle Scholar
Dinh, S. T. and Jelonek, Z.. “Thom isotopy theorem for nonproper maps and computation of sets of stratified generalized critical values”. Discrete Comput. Geom. 65 (2021), 279304 (cit. on pp. 227, 515).Google Scholar
Denef, J. and Lipshitz, L.. “Algebraic power series and diagonals”. J. Number Theory 26 (1987), 4667 (cit. on pp. 50, 56, 430).Google Scholar
DeVore, R. A. and Lorentz, G. G.. Constructive approximation. Vol. 303. Grundlehren der Mathematischen Wissenschaften. Berlin: Springer-Verlag, 1993, x+449 (cit. on p. 331).Google Scholar
Došlić, T.. “Block allocation of a sequential resource”. Ars Mathematica Contemporanea 17 (2019), 7988 (cit. on p. 388).Google Scholar
De Loera, J. A. and Sturmfels, B.. “Algebraic unimodular counting”. Math. Program. 96 (2003), 183203 (cit. on pp. 338, 409).Google Scholar
Du, P.. The Aztec Diamond edge-probability generating function. Masters thesis, Department of Mathematics, University of Pennsylvania. 2011 (cit. on p. 372).Google Scholar
Durrett, R.. Probability: theory and examples. Third edition. Belmont, CA: Duxbury Press, 2004, 497 (cit. on p. 386).Google Scholar
DeVries, T., van der Hoeven, J., and Pemantle, R.. “Effective asymptotics for smooth bivariate generating functions”. Online J. Anal. Comb. 6 (2011) (cit. on p. 262).Google Scholar
de Wolff, T.. “On the Geometry, Topology and Approximation of Amoebas”. PhD thesis. Frankfurt: Johann Wolfgang Goethe-Universität, 2013 (cit. on p. 165).Google Scholar
de Wolff, T.. “Amoebas and their tropicalizations—a survey”. In: Analysis meets geometry. Trends Math. Birkhäuser/Springer, Cham, 2017, 157190 (cit. on p. 165).Google Scholar
Eilenberg, S.. “Singular homology in differentiable manifolds”. Ann. of Math. (2) 48 (1947), 670681 (cit. on p. 464).Google Scholar
Eisenbud, D.. Commutative algebra. Vol. 150. Graduate Texts in Mathematics. New York: Springer-Verlag, 1995, xvi+785 (cit. on p. 227).Google Scholar
Faugère, J.-C. et al. “Computing critical points for invariant algebraic systems”. J. Symbolic Comput. 116 (2023), 365399 (cit. on p. 435).Google Scholar
Flaxman, A., Harrow, A. W., and Sorkin, G. B.. “Strings with maximally many distinct subsequences and substrings”. Electron. J. Combin. 11 (2004), Research Paper 8, 10 pp. (electronic) (cit. on p. 389).Google Scholar
Fayolle, G., Iasnogorodski, R., and Malyshev, V.. Random walks in the quarter-plane. Vol. 40. Applications of Mathematics (New York). Berlin: Springer-Verlag, 1999, xvi+156 (cit. on p. xiv).Google Scholar
Friedrichs, K. and Lewy, H.. “Das Anfangswertproblem einer beliebigen nichtlinearen hyperbolischen Differentialgleichung beliebiger Ordnung in zwei Variablen. Existenz, Eindeutigkeit und Abhängigkeitsbereich der Lösung.” Math. Annalen 99 (1928), 200221 (cit. on p. 368).Google Scholar
Flajolet, P. and Odlyzko, A. M.. “Singularity analysis of generating functions”. SIAM J. Discrete Math. 3 (1990), 216240 (cit. on pp. 71, 75, 84).CrossRefGoogle Scholar
Forsgård, J. et al. “Lopsided approximation of amoebas”. Math. Comp. 88 (2019), 485500 (cit. on p. 165).Google Scholar
Forsberg, M., Passare, M., and Tsikh, A.. “Laurent determinants and arrangements of hyperplane amoebas”. Adv. Math. 151 (2000), 4570 (cit. on pp. 143, 165).Google Scholar
Flajolet, P. and Sedgewick, R.. Analytic combinatorics. Cambridge University Press, 2009, 824 (cit. on pp. xiv, 12, 15, 17, 49, 56, 68, 76, 84, 112, 156, 270, 391, 392).Google Scholar
Furstenberg, H.. “Algebraic functions over finite fields”. J. Algebra 7 (1967), 271277 (cit. on pp. 47, 48).CrossRefGoogle Scholar
Gårding, L.. “Linear hyperbolic partial differential equations with constant coefficients”. Acta Math. 85 (1950), 162 (cit. on pp. 348, 353).Google Scholar
Granet, E. and Essler, F. H. L.. “A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model”. SciPost Phys. 9 (2020), Paper No. 082, 76 (cit. on p. xi).Google Scholar
George, T.. “Grove arctic curves from periodic cluster modular transformations”. Int. Math. Res. Not. IMRN (2021), 1530115336 (cit. on p. xi).Google Scholar
Gessel, I. M.. “Two theorems of rational power series”. Utilitas Math. 19 (1981), 247254 (cit. on p. 56).Google Scholar
Gordon, O., Filmus, Y., and Salzman, O.. “Revisiting the Complexity Analysis of Conflict-Based Search: New Computational Techniques and Improved Bounds”. Proceedings of the Fourteenth International Symposium on Combinatorial Search (SoCS 2021) (2021) (cit. on p. xi).Google Scholar
Griffiths, P. and Harris, J.. Principles of algebraic geometry. Wiley Classics Library. New York: John Wiley & Sons Inc., 1994, xiv+813 (cit. on p. 461).Google Scholar
Gillen, S.. “Critical Points at Infinity for Hyperplanes of Directions”. arXiv preprint arXiv:2210.05748 (2022) (cit. on p. 436).Google Scholar
Goulden, I. P. and Jackson, D. M.. Combinatorial enumeration. Mineola, NY: Dover Publications Inc., 2004, xxvi+569 (cit. on pp. 17, 27, 56, 406).Google Scholar
Gel’fand, I. M., Kapranov, M. M., and Zelevinsky, A. V.. Discriminants, resultants and multidimensional determinants. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA, 2008 (cit. on pp. xv, 164, 165, 243).Google Scholar
Goresky, M. and MacPherson, R.. Stratified Morse theory. Vol. 14. Berlin: Springer-Verlag, 1988, xiv+272 (cit. on pp. 14, 185, 204, 217, 219, 513, 519, 524, 525, 527, 529, 530).Google Scholar
Goresky, M.. “Introduction to the papers of R. Thom and J. Mather”. Bull. AMS 49 (2012), 469474 (cit. on p. 521).Google Scholar
Gordon, G.. “The residue calculus in several complex variables”. Trans. AMS 213 (1975), 127176 (cit. on p. 484).Google Scholar
Guillemin, V. and Pollack, A.. Differential Topology. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1974, xvi+222 (cit. on p. 272).Google Scholar
Gao, Z. and Richmond, L. B.. “Central and local limit theorems applied to asymptotic enumeration. IV. Multivariate generating functions”. J. Comput. Appl. Math. 41 (1992), 177186 (cit. on pp. 9, 386).Google Scholar
Grau Ribas, J. M.. What is the limit of a(n + 1)/a(n)? MathOver-flow. eprint: https://mathoverflow.net/q/389034 (cit. on p. 404).Google Scholar
Greenwood, T. et al. “Asymptotics of coefficients of algebraic series via embedding into rational series (extended abstract)”. Sém. Lothar. Combin. 86B (2022), Art. 30, 12 (cit. on pp. 431, 436).Google Scholar
Greenwood, T.. “Asymptotics of bivariate analytic functions with algebraic singularities”. J. Comb. Theory A 153 (2018), 130 (cit. on p. 403).Google Scholar
Griggs, J. R. et al. “On the number of alignments of k sequences”. Graphs Combin. 6 (1990), 133146 (cit. on p. 409).Google Scholar
Gillis, J., Reznick, B., and Zeilberger, D.. “On elementary methods in positivity theory”. SIAM J. Math. Anal. 14 (1983), 396398 (cit. on p. 376).Google Scholar
Gel’fand, I. M. and Shilov, G. E.. Generalized functions. Vol. 1: Properties and operations. Translated from the Russian by E. Saletan. Reprint of the 1964 original published by Academic Press. Providence, RI: AMS Chelsea Publishing, 2016, xvii+423 (cit. on pp. 366, 375).Google Scholar
Gourdon, X. and Salvy, B.. “Effective asymptotics of linear recurrences with rational coefficients”. In: Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993). Vol. 153. 1996, 145163 (cit. on p. 62).Google Scholar
Gülen, O.. “Hyperbolic polynomials and interior point methods for convex programming”. Math. Oper. Res. 22 (1997), 350377 (cit. on p. 348).Google Scholar
Geronimo, J. S., Woerdeman, H. J., and Wong, C. Y.. “Spectral density functions of bivariable stable polynomials”. Ramanujan J. 56 (2021), 265295 (cit. on p. xi).Google Scholar
Hatcher, A.. Algebraic topology. Cambridge University Press, Cambridge, 2002 (cit. on pp. 465–467, 472, 473, 478).Google Scholar
Hayman, W. K.. “A generalisation of Stirling’s formula”. J. Reine Angew. Math. 196 (1956), 6795 (cit. on pp. xiv, 78, 84).Google Scholar
Henrici, P.. Applied and computational complex analysis. Vol. 1. Wiley Classics Library. New York: John Wiley & Sons Inc., 1988, xviii+682 (cit. on p. 8).Google Scholar
Henrici, P.. Applied and computational complex analysis. Vol. 2. Wiley Classics Library. New York: John Wiley & Sons Inc., 1991, x+662 (cit. on pp. 8, 84, 112).Google Scholar
Hironaka, H.. “Subanalytic sets”. In: Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki. Tokyo: Kinokuniya, 1973, 453493 (cit. on p. 515).Google Scholar
Hirsch, M. W.. Differential topology. Graduate Texts in Mathematics, No. 33. Springer-Verlag, New York-Heidelberg, 1976 (cit. on p. 483).Google Scholar
Hautus, M. L. J. and Klarner, D. A.. “The diagonal of a double power series”. Duke Math. J. 38 (1971), 229235 (cit. on p. 47).Google Scholar
Hubert, E. and Labahn, G.. “Computation of invariants of finite abelian groups”. Mathematics of Computation 85 (2016), 30293050 (cit. on p. 435).Google Scholar
Hauenstein, J. D. and Levandovskyy, V.. “Certifying solutions to square systems of polynomial-exponential equations”. J. Symbolic Comput. 79 (2017), 575593 (cit. on p. 237).Google Scholar
Helmer, M. and Nanda, V.. “Conormal Spaces and Whitney Stratifications”. Foundations of Computational Mathematics (2022) (cit. on pp. 227, 515, 516).Google Scholar
Hörmander, L.. The analysis of linear partial differential operators. I. Vol. 256. Grundlehren der Mathematischen Wissenschaften. Berlin: Springer-Verlag, 1983, ix+391 (cit. on pp. 129, 353).Google Scholar
Hörmander, L.. An introduction to complex analysis in several variables. Third edition. Vol. 7. North-Holland Mathematical Library. Amsterdam: North-Holland Publishing Co., 1990, xii+254 (cit. on pp. 323, 460, 461).Google Scholar
Hirsch, M., Pugh, C., and Shub, M.. “Invariant manifolds”. Lecture Notes in Mathematics 583 (1977) (cit. on p. 204).Google Scholar
Hardy, G. H. and Ramanujan, S.. “Asymptotic formulæ for the distribution of integers of various types [Proc. London Math. Soc. (2) 16 (1917), 112–132]”. In: Collected papers of Srinivasa Ramanujan. AMS Chelsea Publ., Providence, RI, 2000, 245261 (cit. on p. 84).Google Scholar
Hardy, G. H. and Ramanujan, S.. “Une formule asymptotique pour le nombre des partitions de n [Comptes Rendus, 2 Jan. 1917]”. In: Collected papers of Srinivasa Ramanujan. AMS Chelsea Publ., Providence, RI, 2000, 239241 (cit. on p. 84).Google Scholar
Hauenstein, J. D., Rodriguez, J. I., and Sottile, F.. “Numerical computation of Galois groups”. Foundations of Computational Mathematics 18 (2018), 867890 (cit. on p. 327).Google Scholar
Huh, J.. “The maximum likelihood degree of a very affine variety”. Compositio Math. 149 (2013), 12451266 (cit. on p. 430).Google Scholar
Harris, P. E. and Willenbring, J. F.. “Sums of squares of Littlewood–Richardson coefficients and GLn-harmonic polynomials”. In: Symmetry: representation theory and its applications. Springer, 2014, 305326 (cit. on p. 412).Google Scholar
Hwang, H.-K.. “Large deviations for combinatorial distributions. I: Central limit theorems”. Ann. Appl. Probab. 6 (1996), 297319 (cit. on p. 386).Google Scholar
Hwang, H.-K.. “Large deviations of combinatorial distributions. II: Local limit theorems”. Ann. Appl. Probab. 8 (1998), 163181 (cit. on p. 386).Google Scholar
Hwang, H.-K.. “On convergence rates in the central limit theorems for combinatorial structures”. Eur. J. Comb. 19 (1998), 329343 (cit. on p. 386).Google Scholar
Isaacson, E. and Keller, H. B.. Analysis of numerical methods. New York: Dover Publications Inc., 1994, xvi+541 (cit. on p. 37).Google Scholar
Jockusch, W., Propp, J., and Shor, P.. “Random Domino Tilings and the Arctic Circle Theorem”. ArXiv Mathematics e-prints (Jan. 1998). eprint: arXiv:math/9801068 (cit. on p. 15).Google Scholar
Karchyauskas, K.. Homotopy properties of complex algebraic sets. Leningrad: Steklov Institute, 1979 (cit. on p. 478).Google Scholar
Kesten, H.. “Branching Brownian motion with absorption”. Stochastic Processes Appl. 7 (1978), 947 (cit. on p. 29).CrossRefGoogle Scholar
Khera, J., Lundberg, E., and Melczer, S.. “Asymptotic enumeration of lonesum matrices”. Adv. in Appl. Math. 123 (2021), 102118 (cit. on p. xi).Google Scholar
Knuth, D.. The Art of Computer Programming. Vol. I–IV. Upper Saddle River, NJ: Addison-Wesley, 2006 (cit. on p. xiv).Google Scholar
Kenyon, R. and Okounkov, A.. “Limit shapes and the complex Burgers equation”. Acta Math. 199 (2007), 263302 (cit. on p. 373).Google Scholar
Kogan, Y.. “Asymptotic expansions for large closed and loss queueing networks”. Math. Probl. Eng. 8 (2002), 323348 (cit. on p. 310).Google Scholar
Kovačević, M.. “Runlength-limited sequences and shift-correcting codes: asymptotic analysis”. IEEE Trans. Inform. Theory 65 (2019), 48044814 (cit. on p. xi).Google Scholar
Kenyon, R. and Pemantle, R.. “Double-dimers, the Ising model and the hexahedron recurrence”. J. Comb. Theory, ser. A 137 (2016), 2763 (cit. on p. 212).Google Scholar
Krantz, S. G.. Function theory of several complex variables. AMS Chelsea Publishing, Providence, RI, 2001, xvi+564 (cit. on p. 165).Google Scholar
Kogan, Y. and Yakovlev, A.. “Asymptotic analysis for closed multichain queueing networks with bottlenecks”. Queueing Systems Theory Appl. 23 (1996), 235258 (cit. on p. 10).Google Scholar
Kauers, M. and Zeilberger, D.. “The computational challenge of enumerating high-dimensional rook walks”. Advances in Applied Mathematics 47 (2011), 813819 (cit. on p. 421).Google Scholar
Lairez, P.. “Computing periods of rational integrals”. Math. Comp. 85 (2016), 17191752 (cit. on p. 241).Google Scholar
Lasserre, J. B.. An introduction to polynomial and semi-algebraic optimization. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, 2015 (cit. on p. 149).Google Scholar
Lazzeri, F.. “Morse theory on singular spaces”. Astérisque 7–8 (1973), 263268 (cit. on p. 518).Google Scholar
Lee, J. M.. Introduction to smooth manifolds. Vol. 218. Graduate Texts in Mathematics. New York: Springer-Verlag, 2003, xviii+628 (cit. on pp. 127, 476).Google Scholar
Lenz, A. et al. “Exact Asymptotics for Discrete Noiseless Channels”. Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT) (2023) (cit. on p. xi).Google Scholar
Leray, J.. “Le calcul différentiel et intégral sur une variété analytique complexe. (Problème de Cauchy. III)”. Bull. Soc. Math. France 87 (1959), 81180 (cit. on pp. 9, 484).Google Scholar
Lichtin, B.. “The asymptotics of a lattice point problem associated to a finite number of polynomials. I”. Duke Math. J. 63 (1991), 139192 (cit. on p. 10).Google Scholar
Lipshitz, L.. “The diagonal of a D-finite power series is D-finite”. J. Algebra 113 (1988), 373378 (cit. on p. 46).Google Scholar
Lipshitz, L.. “D-finite power series”. J. Algebra 122 (1989), 353373 (cit. on pp. 44, 45, 56).Google Scholar
Larsen, M. and Lyons, R.. “Coalescing particles on an interval”. J. Theoret. Probab. 12 (1999), 201205 (cit. on pp. 15, 33).Google Scholar
Lladser, M.. “Asymptotic enumeration via singularity analysis”. PhD thesis. The Ohio State University, 2003 (cit. on pp. 10, 426).Google Scholar
Lladser, M.. “Uniform formulae for coefficients of meromorphic functions in two variables. I”. SIAM J. Discrete Math. 20 (2006), 811828 (electronic) (cit. on pp. 10, 426).Google Scholar
Lee, K., Melczer, S., and Smolčić, J.. “Homotopy Techniques for Analytic Combinatorics in Several Variables”. In: Proceedings of the 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). 2022, 2734 (cit. on pp. 236, 237, 436).Google Scholar
Limic, V. and Pemantle, R.. “More rigorous results on the Kauffman-Levin model of evolution”. Ann. Probab. 32 (2004), 21492178 (cit. on p. 58).Google Scholar
, D. T. and Teissier, B.. “Geometry of characteristic varieties”. In: Algebraic approach to differential equations. World Sci. Publ., Hackensack, NJ, 2010, 119135 (cit. on p. 518).Google Scholar
Mather, J.. “Notes on topological stability”. Bull. AMS 49 (2012), 475506 (cit. on pp. 521, 522).Google Scholar
Mather, J.. “Notes on topological stability”. Mimeographed notes (1970) (cit. on pp. 126, 216, 217).Google Scholar
Melczer, S.. An Invitation to Analytic Combinatorics: From One to Several Variables. Texts & Monographs in Symbolic Computation. Springer International Publishing, 2021 (cit. on pp. xi, 10, 41, 46, 56, 57, 62, 153, 184, 227, 242–244, 408, 421).Google Scholar
Merlini, D. et al. “On some alternative characterizations of Riordan arrays”. Canad. J. Math. 49 (1997), 301320 (cit. on p. 386).Google Scholar
Mezzarobba, M.. “Rigorous multiple-precision evaluation of D-finite functions in SageMath”. arXiv preprint arXiv:1607.01967 (2016) (cit. on p. 242).Google Scholar
Mezzarobba, M.. “Truncation bounds for differentially finite series”. Ann. H. Lebesgue 2 (2019), 99148 (cit. on p. 237).Google Scholar
Mikhalkin, G.. “Real algebraic curves, the moment map and amoebas”. Ann. of Math. (2) 151 (2000), 309326 (cit. on p. 165).Google Scholar
Mikhalkin, G.. “Amoebas of algebraic varieties and tropical geometry”. In: Different faces of geometry. Vol. 3. Int. Math. Ser. (N. Y.) Kluwer/Plenum, New York, 2004, 257300 (cit. on p. 165).Google Scholar
Milnor, J.. Morse theory. Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51. Princeton, N.J.: Princeton University Press, 1963, vi+153 (cit. on pp. 14, 185, 500, 501, 504, 511, 529).Google Scholar
Mishna, M.. Analytic Combinatorics: A Multidimensional Approach. CRC Press, 2019 (cit. on p. xi).Google Scholar
Mijajlović, Ž. and Malešević, B.. “Differentially transcendental functions”. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), 193201 (cit. on p. 57).Google Scholar
Melczer, S. and Mishna, M.. “Asymptotic lattice path enumeration using diagonals”. Algorithmica 75 (2016), 782811 (cit. on p. xi).Google Scholar
Mostowski, T. and Rannou, E.. “Complexity of the computation of the canonical Whitney stratification of an algebraic set in Cn”. In: Applied algebra, algebraic algorithms and error-correcting codes (New Orleans, LA, 1991). Vol. 539. Lecture Notes in Comput. Sci. Berlin: Springer, 1991, 281291 (cit. on pp. 227, 515).Google Scholar
Melczer, S. and Salvy, B.. “Effective Coefficient Asymptotics of Multivariate Rational Functions via Semi-Numerical Algorithms for Polynomial Systems”. Journal of Symbolic Computation 103 (2021), 234279 (cit. on pp. 62, 229, 236, 237).Google Scholar
Melczer, S. and Smolčić, J.. “Rigorous two dimensional analytic combinatorics in Sage”. 2022 (cit. on pp. 269, 270).Google Scholar
Mumford, D.. Algebraic geometry. I. Classics in Mathematics. Berlin: Springer-Verlag, 1995, x+186 (cit. on p. 228).Google Scholar
Munkres, J. R.. Elements of algebraic topology. Menlo Park, CA: Addison-Wesley Publishing Company, 1984, ix+454 (cit. on pp. 467, 469, 471, 473, 474, 478).Google Scholar
Melczer, S. and Wilson, M. C.. “Higher dimensional lattice walks: connecting combinatorial and analytic behavior”. SIAM J. Disc. Math. 33 (2019), 21402174 (cit. on pp. xi, 318).Google Scholar
Noble, R.. “Asymptotics of a family of binomial sums”. J. Number Theory 130 (2010), 25612585 (cit. on p. 421).Google Scholar
Odlyzko, A. M.. “Asymptotic enumeration methods”. In: Handbook of combinatorics, Vol. 1, 2. Amsterdam: Elsevier, 1995, 10631229 (cit. on pp. xiv, 9, 405).Google Scholar
Orlik, P. and Terao, H.. Arrangements of hyperplanes. Vol. 300. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer-Verlag, 1992, xviii+325 (cit. on pp. 297, 312).Google Scholar
Pantone, J.. “The Asymptotic Number of Simple Singular Vector Tuples of a Cubical Tensor”. Online Journal of Analytic Combinatorics 12 (2017) (cit. on p. xi).Google Scholar
Paris, R. B.. Hadamard expansions and hyperasymptotic evaluation. Vol. 141. Encyclopedia of Mathematics and its Applications. Cambridge: Cambridge University Press, 2011, viii+243 (cit. on p. 422).Google Scholar
Pemantle, R.. “Generating functions with high-order poles are nearly polynomial”. In: Mathematics and computer science (Versailles, 2000). Trends Math. Basel: Birkhäuser, 2000, 305321 (cit. on p. 338).Google Scholar
Pemantle, R.. “Analytic combinatorics in d variables: an overview”. In: Algorithmic probability and combinatorics. Vol. 520. Contemp. Math. Providence, RI: Amer. Math. Soc., 2010, 195220 (cit. on p. 219).Google Scholar
Pham, F.. Singularities of integrals: homology, hyperfunctions and microlocal analysis. Universitext. New York: Springer, 2011, xxii+217 (cit. on pp. 337, 511).Google Scholar
Pignoni, R.. “Density and stability of Morse functions on a stratified space”. Ann. Scuola Nor. Sup.. Pisa, ser. IV 6 (1979), 593608 (cit. on p. 518).Google Scholar
Paris, R. B. and Kaminski, D.. Asymptotics and Mellin-Barnes integrals. Vol. 85. Encyclopedia of Mathematics and its Applications. Cambridge: Cambridge University Press, 2001, xvi+422 (cit. on p. 422).Google Scholar
Poincaré, H.. “Sure les courbes définies par les équations différentielles”. J. Math. Pure et Appliquées 4 (1885), 167244 (cit. on p. 443).Google Scholar
Pólya, G.. “On the number of certain lattice polygons”. J. Combinatorial Theory 6 (1969), 102105 (cit. on p. 405).Google Scholar
Poole, E. G. C.. Introduction to the theory of linear differential equations. Dover Publications, Inc., New York, 1960 (cit. on p. 241).Google Scholar
Passare, M., Pochekutov, D., and Tsikh, A.. “Amoebas of complex hypersurfaces in statistical thermodynamics”. Math. Phys. Anal. Geom. 16 (2013), 89108 (cit. on p. 165).Google Scholar
Petersen, T. K. and Speyer, D.. “An arctic circle theorem for Groves”. J. Combin. Theory Ser. A 111 (2005), 137164 (cit. on p. 370).Google Scholar
Pólya, G. and Szegő, G.. Problems and theorems in analysis. II. Classics in Mathematics. Berlin: Springer-Verlag, 1998, xii+392 (cit. on p. 37).CrossRefGoogle Scholar
Pinna, F. and Viola, C.. “The saddle-point method in CN and the generalized Airy functions”. Bull. Math. Soc. France 147 (2019), 211257 (cit. on p. 131).Google Scholar
Pemantle, R. and Wilson, M. C.. “Asymptotics of multivariate sequences. I. Smooth points of the singular variety”. J. Combin. Theory Ser. A 97 (2002), 129161 (cit. on pp. 10, 15, 219, 289, 337, 421).Google Scholar
Pemantle, R. and Wilson, M. C.. “Asymptotics of multivariate sequences. II. Multiple points of the singular variety”. Combin. Probab. Comput. 13 (2004), 735761 (cit. on pp. 10, 15, 219, 317, 337).Google Scholar
Pemantle, R. and Wilson, M. C.. “Twenty combinatorial examples of asymptotics derived from multivariate generating functions”. SIAM Rev. 50 (2008), 199272 (cit. on pp. 10, 421).Google Scholar
Pemantle, R. and Wilson, M. C.. “Asymptotic expansions of oscillatory integrals with complex phase”. In: Algorithmic probability and combinatorics. Vol. 520. Contemp. Math. Providence, RI: Amer. Math. Soc., 2010, 221240 (cit. on pp. 10, 130).Google Scholar
Petkovšek, M., Wilf, H. S., and Zeilberger, D.. A = B. Wellesley, MA: A K Peters Ltd., 1996, xii+212 (cit. on p. 57).Google Scholar
Rannou, E.. “The complexity of stratification computation”. Discrete Comput. Geom. 19 (1998), 4778 (cit. on pp. 227, 515).Google Scholar
Riesz, M.. “L’intégrale de Riemann-Liouville et le problème de Cauchy”. Acta Mathematica 81 (1949), 1223 (cit. on p. 365).Google Scholar
Rockefellar, R. T.. Convex analysis. Princeton: Princeton University Press, 1966, xiii+451 (cit. on p. 165).Google Scholar
Régnier, M. and Tahi, F.. Generating functions in computational biology. Preprint available at http://algo.inria.fr/regnier/publis/ReTa04.ps. (2005) (cit. on p. 408).Google Scholar
Rubel, L. A.. “Some research problems about algebraic differential equations”. Trans. Amer. Math. Soc. 280 (1983), 4352 (cit. on p. 57).Google Scholar
Rubel, L. A.. “Some research problems about algebraic differential equations. II”. Illinois J. Math. 36 (1992), 659680 (cit. on p. 57).Google Scholar
Rudin, W.. Function theory in polydiscs. W. A. Benjamin, Inc., New York-Amsterdam, 1969 (cit. on p. 165).Google Scholar
Raichev, A. and Wilson, M. C.. “Asymptotics of coefficients of multivariate generating functions: improvements for smooth points”. Electron. J. Combin. 15 (2008), Research Paper 89, 17 (cit. on pp. 10, 289).Google Scholar
Raichev, A. and Wilson, M. C.. “Asymptotics of coefficients of multivariate generating functions: improvements for multiple points”. Online J. Anal. Comb. 6 (2011), 21 (cit. on p. 10).Google Scholar
Ramgoolam, S., Wilson, M. C., and Zahabi, A.. “Quiver asymptotics: free chiral ring”. Journal of Physics A: Mathematical and Theoretical 53 (2020), 105401 (cit. on pp. xi, 412).Google Scholar
Safonov, K. V.. “On power series of algebraic and rational functions in Cn”. J. Math. Anal. Appl. 243 (2000), 261277 (cit. on pp. 49–51, 430).Google Scholar
Shapiro, L. W. et al. “The Riordan group”. Discrete Appl. Math. 34 (1991), 229239 (cit. on p. 421).Google Scholar
Shafarevich, I.. Basic Algebraic Geometry 1: Varieties in Projective Space. Third edition. New York: Springer, 2013, xviii+310 (cit. on p. 182).Google Scholar
Sprugnoli, R.. “Riordan arrays and combinatorial sums”. Discrete Math. 132 (1994), 267290 (cit. on pp. 386, 421).Google Scholar
Scott, A. D. and Sokal, A.. “Complete monotonicity for inverse powers of some combinatorially defined polynomials”. Acta Mathematica 213 (2014), 323392 (cit. on p. 368).Google Scholar
Stanley, R. P.. Catalan numbers. Cambridge University Press, 2015 (cit. on p. 31).Google Scholar
Stanley, R. P.. “Differentiably finite power series”. European J. Combin. 1 (1980), 175188 (cit. on p. 56).Google Scholar
Stanley, R. P.. Enumerative combinatorics. Vol. 1. Vol. 49. Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 1997, xii+325 (cit. on pp. 3, 15, 17, 56, 405, 409).Google Scholar
Stanley, R. P.. Enumerative combinatorics. Vol. 2. Vol. 62. Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 1999, xii+581 (cit. on pp. 41, 42, 47, 56, 436).Google Scholar
Stein, E. M.. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Vol. 43. Princeton Mathematical Series. Princeton, NJ: Princeton University Press, 1993, xiv+695 (cit. on pp. 105, 112, 121, 131).Google Scholar
Sturmfels, B.. Solving systems of polynomial equations. Vol. 97. CBMS regional conference series in mathematics. Providence: American Mathematical Society, 2002, viii+152 (cit. on p. 244).Google Scholar
Szegő, G.. “Über gewisse Potenzreihen mit lauter positiven Koeffizienten”. Math. Z. 37 (1933), 674688 (cit. on pp. 368, 376).Google Scholar
Teissier, B.. “Variétés polaires. II. Multiplicités polaires, sections planes, et conditions de Whitney”. In: Algebraic geometry (La Rábida, 1981). Vol. 961. Lecture Notes in Math. Springer, Berlin, 1982, 314491 (cit. on p. 227).Google Scholar
Theobald, T.. “Computing amoebas”. Experiment. Math. 11 (2002), 513526 (cit. on p. 165).Google Scholar
Timme, S.. “Fast Computation of Amoebas, Coamoebas and Imaginary Projections in Low Dimensions”. MA thesis. Technische Universität Berlin, 2018 (cit. on p. 165).Google Scholar
Tu, L. W.. An introduction to manifolds. Second edition. Universitext. Springer, New York, 2011 (cit. on pp. 447, 461).Google Scholar
Varchenko, A. N.. “Newton polyhedra and estimation of oscillating integrals”. Functional Anal. Appl. 10 (1977), 175196 (cit. on p. 429).Google Scholar
Varchenko, A. and Gelfand, I.. “Combinatorics and topology of configuration of affine hyperplanes in real space”. Funk. Analiz i ego Prilozh. 21 (1987), 1122 (cit. on p. 304).Google Scholar
Vidunas, R.. “Counting derangements and Nash equilibria”. Ann. Comb. 21 (2017), 131152 (cit. on p. xi).Google Scholar
van Lint, J. H. and Wilson, R. M.. A Course in Combinatorics. Second edition. Cambridge: Cambridge University Press, 2001, xiv+602 (cit. on p. 17).Google Scholar
Voisin, C.. Hodge theory and complex algebraic geometry. I. Vol. 76. Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2002 (cit. on pp. 477, 478).Google Scholar
Wagner, D. G.. “Multivariate Stable Polynomials: theory and application”. Bull. AMS 48 (2011), 5384 (cit. on p. 379).Google Scholar
Wang, H.-Y.. “A bivariate rational Laurent series of interest”. Personal communication (2022) (cit. on pp. 274, 276).Google Scholar
Ward, M.. “Asymptotic rational approximation to Pi: Solution of an unsolved problem posed by Herbert Wilf”. Disc. Math. Theor. Comp. Sci. AM (2010), 591602 (cit. on p. 85).Google Scholar
Warner, F. W.. Foundations of differentiable manifolds and Lie groups. Vol. 94. Graduate Texts in Mathematics. New York: Springer-Verlag, 1983, ix+272 (cit. on pp. 455, 456, 461).Google Scholar
Waterman, M. S.. “Applications of combinatorics to molecular biology”. In: Handbook of combinatorics, Vol. 1, 2. Amsterdam: Elsevier, 1995, 19832001 (cit. on p. 408).Google Scholar
Whitney, H.. “Local properties of analytic varieties”. In: Differential and Combinatorial Topology. Princeton, NJ: Princeton University Press, 1965 (cit. on p. 521).Google Scholar
Whitney, H.. “Tangents to an analytic variety”. Annals Math. 81 (1965), 496549 (cit. on p. 515).Google Scholar
Wilson, M. C.. “Asymptotics for generalized Riordan arrays”. In: 2005 International Conference on Analysis of Algorithms. Discrete Math. Theor. Comput. Sci. Proc., AD. Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2005, 323333 (cit. on pp. 10, 388, 421).Google Scholar
Wilf, H. S.. generatingfunctionology. Third edition. Wellesley, MA: A. K. Peters, 2006, x+245 (cit. on pp. 12, 17, 405).Google Scholar
Wilson, M. C.. “Diagonal Asymptotics for Products of Combinatorial Classes”. Combinatorics, Probability and Computing 24 (2015), 354372 (cit. on pp. xi, 421).Google Scholar
Wong, R.. Asymptotic approximations of integrals. Vol. 34. Classics in Applied Mathematics. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2001, xviii+543 (cit. on pp. 112, 131).Google Scholar
Wimp, J. and Zeilberger, D.. “Resurrecting the asymptotics of linear recurrences”. J. Math. Anal. Appl. 111 (1985), 162176 (cit. on p. 57).Google Scholar
Zeilberger, D.. “Sister Celine’s technique and its generalizations”. J. Math. Anal. Appl. 85 (1982), 114145 (cit. on p. 56).Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Robin Pemantle, University of Pennsylvania, Mark C. Wilson, University of Massachusetts, Amherst, Stephen Melczer, University of Waterloo, Ontario
  • Book: Analytic Combinatorics in Several Variables
  • Online publication: 08 February 2024
  • Chapter DOI: https://doi.org/10.1017/9781108874144.023
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Robin Pemantle, University of Pennsylvania, Mark C. Wilson, University of Massachusetts, Amherst, Stephen Melczer, University of Waterloo, Ontario
  • Book: Analytic Combinatorics in Several Variables
  • Online publication: 08 February 2024
  • Chapter DOI: https://doi.org/10.1017/9781108874144.023
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Robin Pemantle, University of Pennsylvania, Mark C. Wilson, University of Massachusetts, Amherst, Stephen Melczer, University of Waterloo, Ontario
  • Book: Analytic Combinatorics in Several Variables
  • Online publication: 08 February 2024
  • Chapter DOI: https://doi.org/10.1017/9781108874144.023
Available formats
×