{
  "id": "2307.04839",
  "version": "v1",
  "published": "2023-07-10T18:16:02.000Z",
  "updated": "2023-07-10T18:16:02.000Z",
  "title": "Two classes of posets with real-rooted chain polynomials",
  "authors": [
    "Christos A. Athanasiadis",
    "Katerina Kalampogia-Evangelinou"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. It has been a challenging open problem to determine which posets have real-rooted chain polynomials. Two new classes of posets with this property, namely those of all rank-selected subposets of Cohen-Macaulay simplicial posets and all noncrossing partition lattices associated to irreducible finite Coxeter groups, are presented here. The first result generalizes one of Brenti and Welker. As a special case, the descent enumerator of permutations of the set $\\{1, 2,\\dots,n\\}$ which have ascents at specified positions is shown to be real-rooted, hence unimodal, and a good estimate for the location of the peak is deduced.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-10T18:16:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05E45",
      "06A07",
      "26C10"
    ],
    "keywords": [
      "real-rooted chain polynomials",
      "finite poset enumerate chains",
      "cohen-macaulay simplicial posets",
      "first result generalizes",
      "irreducible finite coxeter groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}