Distributions of Statistics over Pattern-Avoiding Permutations
Combinatorics
2019-07-24 v3
Abstract
We consider the distribution of ascents, descents, peaks, valleys, double ascents, and double descents over permutations avoiding a set of patterns. Many of these statistics have already been studied over sets of permutations avoiding a single pattern of length 3. However, the distribution of peaks over 321-avoiding permutations is new and we relate it statistics on Dyck paths. We also obtain new interpretations of a number of well-known combinatorial sequences by studying these statistics over permutations avoiding two patterns of length 3.
Cite
@article{arxiv.1812.07112,
title = {Distributions of Statistics over Pattern-Avoiding Permutations},
author = {Michael Bukata and Ryan Kulwicki and Nicholas Lewandowski and Lara Pudwell and Jacob Roth and Teresa Wheeland},
journal= {arXiv preprint arXiv:1812.07112},
year = {2019}
}
Comments
27 pages, 2 figures, 5 tables