论文信息 - Consecutive patterns in permutations

Consecutive patterns in permutations

In this paper we study the distribution of the number of occurrences of a permutation σ as a subword among all permutations in Sn. We solve the problem in several cases depending on the shape of σ by obtaining the corresponding bivariate exponential generating functions as solutions of certain linear differential equations with polynomial coefficients. Our method is based on the representation of permutations as increasing binary trees and on symbolic methods.

Marc Noy | Sergi Elizalde | M. Noy | S. Elizalde

[1] Rodica Simion,et al. Restricted Permutations , 1985, Eur. J. Comb..

[2] I. Goulden,et al. Combinatorial Enumeration , 2004 .

[3] L. Carlitz,et al. Enumeration of permutations by rises, falls, rising maxima and falling maxima , 1974 .

[4] L. CARLITZ. Enumeration of permutations by rises and cycle structure. , 1973 .

[5] D. Zeilberger,et al. The Enumeration of Permutations with a Prescribed Number of “Forbidden” Patterns , 1996, math/9808080.

[6] Philippe Flajolet,et al. Analytic combinatorics of non-crossing configurations , 1999, Discret. Math..

[7] D. Zeilberger,et al. The Goulden—Jackson cluster method: extensions, applications and implementations , 1998, math/9806036.

[8] Philippe Flajolet,et al. Patterns in random binary search trees , 1997, Random Struct. Algorithms.

[9] Philippe Flajolet,et al. An introduction to the analysis of algorithms , 1995 .

[10] Luc Devroye,et al. Limit Laws for Local Counters in Random Binary Search Tree , 1991, Random Struct. Algorithms.

[11] Sergey Kitaev. Multi-avoidance of generalised patterns , 2003, Discret. Math..

[12] Eric Babson,et al. Generalized permutation patterns and a classification of the Mahonian statistics , 2000 .

[13] Anders Claesson. GENERALISED PATTERN AVOIDANCE , 2000 .

[14] Anders Claesson,et al. Generalized Pattern Avoidance , 2001, Eur. J. Comb..

[15] Thomas Spencer,et al. Self-avoiding walk in 5 or more dimensions , 1985 .