Skip to main content Accessibility help
×
Home
Hostname: page-component-5d6d958fb5-c6lpx Total loading time: 0.394 Render date: 2022-11-29T10:25:02.278Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Restricted patience sorting and barred pattern avoidance

Published online by Cambridge University Press:  05 October 2010

Alexander Burstein
Affiliation:
Department of Mathematics, Howard University, Washington, DC 20059, USA
Isaiah Lankham
Affiliation:
Department of Mathematics, Simpson University, Redding, CA 96003, USA
Steve Linton
Affiliation:
University of St Andrews, Scotland
Nik Ruškuc
Affiliation:
University of St Andrews, Scotland
Vincent Vatter
Affiliation:
Dartmouth College, New Hampshire
Get access
Type
Chapter
Information
Permutation Patterns , pp. 233 - 258
Publisher: Cambridge University Press
Print publication year: 2010

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

[1] M. H., Albert, S., Linton, and N., Ruškuc. The insertion encoding of permutations. Electron. J. Combin., 12(1):Research paper 47, 31 pp., 2005.Google Scholar
[2] D., Aldous and P., Diaconis. Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem. Bull. Amer. Math. Soc. (N.S.), 36(4):413–432, 1999.Google Scholar
[3] S., Bespamyatnikh and M., Segal. Enumerating longest increasing subsequences and patience sorting. Inform. Process. Lett., 76(1-2):7–11, 2000.Google Scholar
[4] M., Bóna. Combinatorics of permutations. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2004.Google Scholar
[5] A., Burstein and I., Lankham. Combinatorics of patience sorting piles. Sém. Lothar. Combin., 54A:Art. B54Ab, 19 pp., 2005/07.Google Scholar
[6] A., Burstein and I., Lankham. A geometric form for the extended patience sorting algorithm. Adv. in Appl. Math., 36(2):106–117, 2006.Google Scholar
[7] A., Claesson. Generalized pattern avoidance. European J. Combin., 22(7):961–971, 2001.Google Scholar
[8] A., Claesson and T., Mansour. Counting occurrences of a pattern of type (1, 2) or (2, 1) in permutations. Adv. in Appl. Math., 29(2):293–310, 2002.Google Scholar
[9] A., Claesson and T., Mansour. Enumerating permutations avoiding a pair of Babson-Steingrímsson patterns. Ars Combin., 77:17–31, 2005.Google Scholar
[10] S., Dulucq, S., Gire, and O., Guibert. A combinatorial proof of J. West's conjecture. Discrete Math., 187(1-3):71–96, 1998.Google Scholar
[11] S., Dulucq, S., Gire, and J., West. Permutations with forbidden subsequences and nonseparable planar maps. Discrete Math., 153(1-3):85–103, 1996.Google Scholar
[12] C. L., Mallows. Problem 62-2, patience sorting. SIAM Review, 4:148–149, 1962. Solution in Vol. 5 (1963), 375–376.Google Scholar
[13] A., Marcus and G., Tardos. Excluded permutation matrices and the Stanley-Wilf conjecture. J. Combin. Theory Ser. A, 107(1):153–160, 2004.Google Scholar
[14] A., Price. Packing densities of layered patterns. PhD thesis, Univ. of Pennsylvania, 1997.
[15] B. E., Sagan. The Symmetric Group, volume 203 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 2001.Google Scholar
[16] L. W., Shapiro, S., Getu, W. J., Woan, and L. C., Woodson. The Riordan group. Discrete Appl. Math., 34(1-3):229–239, 1991.Google Scholar
[17] N. J. A., Sloane. The On-line Encyclopedia of Integer Sequences. Available online at http://www.research.att.com/∼njas/sequences/.
[18] R. P., Stanley. Enumerative combinatorics. Vol. 2, volume 62 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1999.Google Scholar
[19] G., Viennot. Une forme géométrique de la correspondance de Robinson-Schensted. In Combinatoire et représentation du groupe symétrique (Actes Table Ronde CNRS, Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976), pages 29–58. Lecture Notes in Math., Vol. 579. Springer, Berlin, 1977.Google Scholar
[20] J., West. Permutations with forbidden subsequences and stack-sortable permutations. PhD thesis, M.I.T., 1990.
[21] A., Woo and A., Yong. When is a Schubert variety Gorenstein? Adv. Math., 207(1):205–220, 2006.Google Scholar
[22] A., Woo and A., Yong. Governing singularities of Schubert varieties. J. Algebra, 320(2):495–520, 2008.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.

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.

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.

Available formats
×