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arXiv:1812.07112 [math.CO]AbstractReferencesReviewsResources

Distributions of Statistics over Pattern-Avoiding Permutations

Michael Bukata, Ryan Kulwicki, Nicholas Lewandowski, Lara Pudwell, Jacob Roth, Teresa Wheeland

Published 2018-12-18Version 1

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.

Comments: 26 pages, 2 figures, 4 tables
Categories: math.CO
Subjects: 05A05
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