{
  "id": "2103.06635",
  "version": "v1",
  "published": "2021-03-11T12:21:32.000Z",
  "updated": "2021-03-11T12:21:32.000Z",
  "title": "On Hankel Determinants for Dyck Paths with Peaks Avoiding Multiple Classes of Heights",
  "authors": [
    "Hsu-Lin Chien",
    "Sen-Peng Eu",
    "Tung-Shan Fu"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For any integer $m\\ge 2$ and a set $V\\subset \\{1,\\dots,m\\}$, let $(m,V)$ denote the union of congruence classes of the elements in $V$ modulo $m$. We study the Hankel determinants for the number of Dyck paths with peaks avoiding the heights in the set $(m,V)$. For any set $V$ of even elements of an even modulo $m$, we give an explicit description of the sequence of Hankel determinants in terms of subsequences of arithmetic progression of integers. There are numerous instances for varied $(m,V)$ with periodic sequences of Hankel determinants. We present a sufficient condition for the set $(m,V)$ such that the sequence of Hankel determinants is periodic, including even and odd modulus $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-11T12:21:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B36",
      "15A15",
      "05B20",
      "05A19"
    ],
    "keywords": [
      "hankel determinants",
      "peaks avoiding multiple classes",
      "dyck paths",
      "odd modulus",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}