Total occurrence statistics on restricted permutations
Combinatorics
2013-05-15 v1
Abstract
We study the total number of occurrences of several vincular (also called generalized) patterns and other statistics, such as the major index and the Denert statistic, on permutations avoiding a pattern of length 3, extending results of Bona (2010, 2012) and Homberger (2012). In particular, for 2-3-1-avoiding permutations, we find the total number of occurrences of any vincular pattern of length 3. In some cases the answer is given by simple expressions involving binomial coefficients. The tools we use are bijections with Dyck paths, generating functions, and block decompositions of permutations.
Cite
@article{arxiv.1305.3177,
title = {Total occurrence statistics on restricted permutations},
author = {Alexander Burstein and Sergi Elizalde},
journal= {arXiv preprint arXiv:1305.3177},
year = {2013}
}
Comments
To appear in Pure Math. Appl. (PU.M.A.)