Four classes of pattern-avoiding permutations under one roof: Generating trees with two labels

Electronic Journal of Combinatorics

Volumn 9, Issue 2, 2002, Pages

  Bousquet Mélou, Mireille ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 32844454881     PISSN: 10778926     EISSN: 10778926     Source Type: Journal    
DOI: 10.37236/1691     Document Type: Article

References (39)

1. E. Babson and E. Steingrimsson. Generalized permutation patterns and a classification of the Mahonian statistics. Sem. Lothar. Combin., 44:Art. B44b, 18 pp. (electronic), 2000.
2. C. Banderier, M. Bousquet-Melou, A. Denise, P. Flajolet, D. Gardy, and D. GouyouBeauchamps. Generating functions for generating trees. Discrete Math., 246(1-3):29-55, 2002. Formal Power Series and Algebraic Combinatorics (Barcelona, 1999).
3. C. Banderier and P. Flajolet. Basic analytic combinatorics of directed lattice paths. Theoret. Comput. Sei., 281(1-2):37-80, 2002.
4. R. J. Baxter. Dichromatic polynomials and Potts models summed over rooted maps. Ann. Comb., 5(1):17-36, 2001.
5. M. Bóna. Exact enumeration of 1342-avoiding permutations: a close link with labeled trees and planar maps. J. Combin. Theory Ser. A, 80(2):257-272, 1997.
6. M. Bousquet-Mélou. Three osculating walkers. In preparation.
7. M. Bousquet-Mélou. Walks in the quarter plane: Kreweras' algebraic model. In preparation.
8. M. Bousquet-Mélou. Counting walks in the quarter plane. In Mathematics and computer science, II (Versailles, 2002), Trends Math., pages 49-67. Birkhäuser, Basel, 2002.
9. M. Bousquet-Mélou and M. Petkovsek. Linear recurrences with constant coefficients: the multivariate case. Discrete Math., 225(1-3):51-75, 2000. Formal Power Series and Algebraic Combinatorics (Toronto, ON, 1998).
10. M. Bousquet-Melou and M. Petkovsek. Walks confined in a quadrant are not always D-finite. Theoret. Comput. Sei., 307:257-276, 2003.
11. F. R. K. Chung, R. L. Graham, V. E. Hoggatt, Jr., and M. Kleiman. The number of Baxter permutations. J. Combin. Theory Ser. A, 24(3):382-394, 1978.
12. 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.
13. S. Dulucq and O. Guibert. Stack words, standard tableaux and Baxter permutations. Discrete Math., 157(1-3):91-106, 1996. Formal Power Series and Algebraic Combinatorics (New Brunswick, NJ, 1994).
14. G. Fayolle, R. lasnogorodski, and V. Malyshev. Random walks in the quarter-plane: Algebraic methods, boundary value problems and applications, volume 40 of Applications of Mathematics. Springer-Verlag, Berlin, 1999.
15. d and permutations with no long ascending subsequences. Electron. J. Combin., 5(l):Research Paper 2, 11 pp. (electronic), 1998.
16. I. M. Gessel. Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A, 53(2):257-285, 1990.
17. S. Gire. Arbres, permutations à motifs exclus et cartes planaires : quelques problemes algorithmiques et combinatoires. PhD thesis, LaBRI, Université Bordeaux 1, 1993.
18. D. Gouyou-Beauchamps. Standard Young tableaux of height 4 and 5. European J. Combin., 10(l):69-82, 1989.
19. O. Guibert. Combinatoire des permutations à motifs exclus, en liaison avec mots, cartes planaires et tableaux de Young. PhD thesis, LaBRI, Université Bordeaux 1, 1995.
20. O. Guibert and E. Pergola. Enumeration of vexillary involutions which are equal to their mirror/complement. Discrete Math., 224(l-3):281-287, 2000.
21. O. Guibert, E. Pergola, and R. Pinzani. Vexillary involutions are enumerated by Motzkin numbers. Ann. Comb., 5(2): 153-174, 2001.
22. A. D. Jaggard. Prefix exchanging and pattern avoidance for involutions. Electron. J. Combin., 9(2):Research Paper 16, 2003.
23. C. Krattenthaler. Permutations with restricted patterns and Dyck paths. Adv. in Appl. Math., 27(2-3):510-530, 2001.
24. D. Kremer. Permutations with forbidden subsequences and a generalized Schröder number. Discrete Math., 218(1-3):121-130, 2000.
25. A. Lascoux and M.-P. Schutzenberger. Schubert polynomials and the Littlewood-Richardson rule. Lett. Math. Phys., 10(2-3):111-124, 1985.
26. L. Lipshitz. The diagonal of a D-finite power series is D-finite. J. Algebra, 113(2):373-378, 1988.
27. L. Lipshitz. D-finite power series. J. Algebra, 122:353-373, 1989.
28. C. L. Mallows. Baxter permutations rise again. J. Combin. Theory Ser. A, 27(3):394-396, 1979.
29. M. Petkovšek, H. S. Wilf, and D. Zeilberger. A = B. A K Peters Ltd., Wellesley, MA, 1996.
30. C. Schensted. Longest increasing and decreasing subsequences. Canad. J. Math., 13:179-191, 1961.
31. N. J. A. Sloane and S. Plouffe. The encyclopedia of integer sequences. Academic Press Inc., San Diego, CA, 1995. http://www.research.att.com/~njas/sequences/index.html.
32. Z. Stankova. Classification of forbidden subsequences of length 4. European J. Cornbin., 17(5):501-517, 1996.
33. Z. Stankova and J. West. A new class of Wilf-equivalent permutations. J. Algebraic Combin., 15(3):271-290, 2002.
34. R. P. Stanley. Differentiably finite power series. European J. Combin., 1:175-188, 1980.
35. R. P. Stanley. Enumerative combinatorics. Vol. 2, volume 62 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1999.
36. G. Viennot. A bijective proof for the number of Baxter permutations. 3rd Séminaire lotharingien de Combinatoire, Le Klebach, 1981.
37. J. West. Permutations with forbidden subsequences, and stack-sortable permutations. PhD thesis, MIT, 1990.
38. J. West. Generating trees and the Catalan and Schröder numbers. Discrete Math., 146(l-3):247-262, 1995.
39. D. Zeilberger. The umbral transfer-matrix method: I. Foundations. J. Comb. Theory, Ser. A, 91:451-463, 2000.