{
  "id": "2205.03796",
  "version": "v1",
  "published": "2022-05-08T06:36:37.000Z",
  "updated": "2022-05-08T06:36:37.000Z",
  "title": "Chain enumeration, partition lattices and polynomials with only real roots",
  "authors": [
    "Christos A. Athanasiadis",
    "Katerina Kalampogia-Evangelinou"
  ],
  "comment": "19 pages, zero figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. The chain polynomials of the partition lattices and their standard type $B$ analogues are shown to have only real roots. The real-rootedness of the chain polynomial is conjectured for all geometric lattices and is shown to be preserved by the pyramid and the prism operations on Cohen--Macaulay posets. As a result, new families of convex polytopes whose face lattices have real-rooted chain polynomials are presented. An application to the face enumeration of the second barycentric subdivision of the boundary complex of the simplex is also included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-08T06:36:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A18",
      "05E45",
      "06A07",
      "26C10"
    ],
    "keywords": [
      "partition lattices",
      "real roots",
      "chain polynomial",
      "chain enumeration",
      "finite poset enumerate chains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}