{
  "id": "2009.02272",
  "version": "v1",
  "published": "2020-09-04T16:10:08.000Z",
  "updated": "2020-09-04T16:10:08.000Z",
  "title": "Face numbers of barycentric subdivisions of cubical complexes",
  "authors": [
    "Christos A. Athanasiadis"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The $h$-polynomial of the barycentric subdivision of any $n$-dimensional cubical complex with nonnegative cubical $h$-vector is shown to have only real roots and to be interlaced by the Eulerian polynomial of type $B_n$. This result applies to barycentric subdivisions of shellable cubical complexes and, in particular, to barycentric subdivisions of cubical convex polytopes and answers affirmatively a question of Brenti, Mohammadi and Welker.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-04T16:10:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45"
    ],
    "keywords": [
      "barycentric subdivision",
      "face numbers",
      "dimensional cubical complex",
      "real roots",
      "eulerian polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}