Restricted patience sorting and barred pattern avoidance  pp. 233-258

Restricted patience sorting and barred pattern avoidance

By Alexander Burstein and Isaiah Lankham
[10] S. Dulucq , S. Gire , and O. Guibert . A combinatorial proof of J. West's conjecture. Discrete Math., 187(1-3):71–96, 1998.
[11] S. Dulucq , S. Gire , and J. West . Permutations with forbidden subsequences and nonseparable planar maps. Discrete Math., 153(1-3):85–103, 1996.
[12] C. L. Mallows . Problem 62-2, patience sorting. SIAM Review, 4:148–149, 1962. Solution in Vol. 5 (1963), 375–376.
[13] A. Marcus and G. Tardos . Excluded permutation matrices and the Stanley-Wilf conjecture. J. Combin. Theory Ser. A, 107(1):153–160, 2004.
[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.
[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.
[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.
[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.
[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.
[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.
[22] A. Woo and A. Yong . Governing singularities of Schubert varieties. J. Algebra, 320(2):495–520, 2008.
[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.
[3] S. Bespamyatnikh and M. Segal . Enumerating longest increasing subsequences and patience sorting. Inform. Process. Lett., 76(1-2):7–11, 2000.
[4] M. Bóna . Combinatorics of permutations. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2004.
[5] A. Burstein and I. Lankham . Combinatorics of patience sorting piles. Sém. Lothar. Combin., 54A:Art. B54Ab, 19 pp., 2005/07.
[6] A. Burstein and I. Lankham . A geometric form for the extended patience sorting algorithm. Adv. in Appl. Math., 36(2):106–117, 2006.
[7] A. Claesson . Generalized pattern avoidance. European J. Combin., 22(7):961–971, 2001.
[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.
[9] A. Claesson and T. Mansour . Enumerating permutations avoiding a pair of Babson-Steingrímsson patterns. Ars Combin., 77:17–31, 2005.