{
"id": "1812.10738",
"version": "v1",
"published": "2018-12-27T15:02:22.000Z",
"updated": "2018-12-27T15:02:22.000Z",
"title": "Revisiting pattern avoidance and quasisymmetric functions",
"authors": [
"Jonathan Bloom",
"Bruce Sagan"
],
"comment": "25 pages",
"categories": [
"math.CO"
],
"abstract": "Let S_n be the nth symmetric group. Given a set of permutations Pi we denote by S_n(Pi) the set of permutations in S_n which avoid Pi in the sense of pattern avoidance. Consider the generating function Q_n(Pi) = sum_pi F_{Des pi} where the sum is over all pi in S_n(Pi) and F_{Des pi} is the fundamental quasisymmetric function corresponding to the descent set of pi. Hamaker, Pawlowski, and Sagan introduced Q_n(Pi) and studied its properties, in particular, finding criteria for when this quasisymmetric function is symmetric or even Schur nonnegative for all n >= 0. The purpose of this paper is to continue their investigation answering some of their questions, proving one of their conjectures, as well as considering other natural questions about Q_n(Pi). In particular we look at Pi of small cardinality, superstandard hooks, partial shuffles, Knuth classes, and a stability property.",
"revisions": [
{
"version": "v1",
"updated": "2018-12-27T15:02:22.000Z"
}
],
"analyses": {
"subjects": [
"05E05",
"05A05"
],
"keywords": [
"revisiting pattern avoidance",
"nth symmetric group",
"fundamental quasisymmetric function",
"descent set",
"stability property"
],
"note": {
"typesetting": "TeX",
"pages": 25,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}