Journal of Integer Sequences, Vol. 22 (2019), Article 19.2.6

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 University
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.

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(Concerned with sequences A000108 A001263 A007318 A008292 A034839 A034867 A076791 A091156 A091894 A092107 A093560 A109446 A119462 A236406 A299927.)

Received December 18 2018; revised version received March 25 2019. Published in Journal of Integer Sequences, March 28 2019.

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