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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
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Permutation Patterns , pp. 233 - 258
Publisher: Cambridge University Press
Print publication year: 2010

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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

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