Distributions of Statistics over Pattern-Avoiding Permutations
Michael Bukata, Ryan Kulwicki, Nicholas Lewandowski,
Lara Pudwell, Jacob Roth, and Teresa Wheeland
Department of Mathematics and Statistics
Valparaiso, IN 46383
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 to 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.
Full version: pdf,
(Concerned with sequences
Received December 18 2018; revised version received March 25 2019.
Published in Journal of Integer Sequences, March 28 2019.
Journal of Integer Sequences home page