Distributions of Statistics over PatternAvoiding Permutations
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 321avoiding permutations is new and we relate it statistics on Dyck paths. We also obtain new interpretations of a number of wellknown combinatorial sequences by studying these statistics over permutations avoiding two patterns of length 3.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 DOI:
 10.48550/arXiv.1812.07112
 arXiv:
 arXiv:1812.07112
 Bibcode:
 2018arXiv181207112B
 Keywords:

 Mathematics  Combinatorics;
 05A05
 EPrint:
 27 pages, 2 figures, 5 tables