{
"id": "1901.02906",
"version": "v1",
"published": "2019-01-09T19:04:24.000Z",
"updated": "2019-01-09T19:04:24.000Z",
"title": "Fixed Points of Parking Functions",
"authors": [
"Jon McCammond",
"Hugh Thomas",
"Nathan Williams"
],
"comment": "37 pages",
"categories": [
"math.CO"
],
"abstract": "We define an action of words in $[m]^n$ on $\\mathbb{R}^m$ to give a new characterization of rational parking functions---they are exactly those words whose action has a fixed point. We use this viewpoint to give a simple definition of Gorsky, Mazin, and Vazirani's zeta map on rational parking functions when m and n are coprime, and prove that this zeta map is invertible. A specialization recovers Loehr and Warrington's sweep map on rational Dyck paths.",
"revisions": [
{
"version": "v1",
"updated": "2019-01-09T19:04:24.000Z"
}
],
"analyses": {
"subjects": [
"05A19",
"55M20",
"05E10",
"05A05"
],
"keywords": [
"fixed point",
"vaziranis zeta map",
"warringtons sweep map",
"rational dyck paths",
"rational parking functions-they"
],
"note": {
"typesetting": "TeX",
"pages": 37,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}