Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-22T12:19:18.175Z Has data issue: false hasContentIssue false
  • English
  • Français

Level Rings Arising from Meet-Distributive Meet-Semilattices

Published online by Cambridge University Press:  11 January 2016

Jürgen Herzog  and
Takayuki Hibi
Jürgen Herzog
Affiliation:
Fachbereich Mathematik und Informatik, Universitäat Duisburg-Essen, Campus Essen 45117 Essen, Germanyjuergen.herzog@uni-essen.de
Takayuki Hibi
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka Osaka 560-0043, Japanhibi@math.sci.osaka-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The homogenized ideal dual complex of an arbitrary meet-semilattice is introduced and described explicitly. Meet-distributive meet-semilattices whose homogenized ideal dual complex is level are characterized.

Keywords

13D0213H1006A1206D99
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 181 , March 2006 , pp. 29 - 39
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

References

[1] Bruns, W. and Herzog, J., Cohen-Macaulay rings, Revised Edition, Cambridge University Press, 1996.Google Scholar
[2] Eagon, J. and Reiner, V., Resolutions of Stanley-Reisner rings and Alexander duality, J. Pure Appl. Algebra, 130 (1998), 265–275.Google Scholar
[3] Edelman, P., Abstract convexity and meet-distributive lattices, Combinatorics and ordered sets (Arcata, Calif., 1985), Contemp. Math. 57, Amer. Math. Soc., Providence, RI (1986), pp. 127–150.Google Scholar
[4] Herzog, J., Hibi, T. and Zheng, X., Dirac’s theorem on chordal graphs and Alexander duality, Europ. J. Combin., 25 (2004), 949–960.Google Scholar
[5] Herzog, J., Hibi, T. and Zheng, X., The monomial ideal of a finite meet-semilattice, to appear, Trans. Amer. Math. Soc.Google Scholar
[6] Herzog, J. and Hibi, T., Distributive Lattices, Bipartite Graphs and Alexander Duality, to appear, J. Alg. Combin.Google Scholar
[7] Stanley, R. P., Enumerative Combinatorics, Volume I, Wadsworth & Brooks/Cole, Monterey, CA, 1986.Google Scholar
[8] Stanley, R. P., Combinatorics and Commutative Algebra, Second Edition, Birkhaäuser, Boston, MA, 1996.Google Scholar