Distributions of Statistics over Pattern-Avoiding 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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2018
- DOI:
- 10.48550/arXiv.1812.07112
- arXiv:
- arXiv:1812.07112
- Bibcode:
- 2018arXiv181207112B
- Keywords:
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- Mathematics - Combinatorics;
- 05A05
- E-Print:
- 27 pages, 2 figures, 5 tables