{
"id": "1812.07112",
"version": "v1",
"published": "2018-12-18T00:15:11.000Z",
"updated": "2018-12-18T00:15:11.000Z",
"title": "Distributions of Statistics over Pattern-Avoiding Permutations",
"authors": [
"Michael Bukata",
"Ryan Kulwicki",
"Nicholas Lewandowski",
"Lara Pudwell",
"Jacob Roth",
"Teresa Wheeland"
],
"comment": "26 pages, 2 figures, 4 tables",
"categories": [
"math.CO"
],
"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.",
"revisions": [
{
"version": "v1",
"updated": "2018-12-18T00:15:11.000Z"
}
],
"analyses": {
"subjects": [
"05A05"
],
"keywords": [
"statistics",
"pattern-avoiding permutations",
"distribution",
"permutations avoiding",
"well-known combinatorial sequences"
],
"note": {
"typesetting": "TeX",
"pages": 26,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}