# Distributions of Statistics over Pattern-Avoiding Permutations

@article{Bukata2018DistributionsOS, title={Distributions of Statistics over Pattern-Avoiding Permutations}, author={Michael Bukata and Ryan Kulwicki and Nicholas Lewandowski and Lara K. Pudwell and Jacob Roth and Teresa Wheeland}, journal={J. Integer Seq.}, year={2018}, volume={22}, pages={19.2.6} }

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…

## 10 Citations

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