{
  "id": "2009.10655",
  "version": "v1",
  "published": "2020-09-22T16:12:57.000Z",
  "updated": "2020-09-22T16:12:57.000Z",
  "title": "Log-concavity of the Excedance Enumerators in positive elements of Type A and Type B Coxeter Groups",
  "authors": [
    "Hiranya Kishore Dey"
  ],
  "comment": "17 Pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The classical Eulerian Numbers $A_{n,k}$ are known to be log-concave. Let $P_{n,k}$ and $Q_{n,k}$ be the number of even and odd permutations with $k$ excedances. In this paper, we show that $P_{n,k}$ and $Q_{n,k}$ are log-concave. For this, we introduce the notion of strong synchronisation and ratio-alternating which are motivated by the notion of synchronisation and ratio-dominance, introduced by Gross, Mansour, Tucker and Wang in 2014. We show similar results for Type B Coxeter Groups. We finish with some conjectures to emphasize the following: though strong synchronisation is stronger than log-concavity, many pairs of interesting combinatorial families of sequences seem to satisfy this property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-22T16:12:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A20"
    ],
    "keywords": [
      "coxeter groups",
      "excedance enumerators",
      "positive elements",
      "log-concavity",
      "strong synchronisation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}