{
  "id": "2410.08812",
  "version": "v1",
  "published": "2024-10-11T13:50:54.000Z",
  "updated": "2024-10-11T13:50:54.000Z",
  "title": "A convex ear decomposition of the augmented Bergman complex of a matroid",
  "authors": [
    "Christos A. Athanasiadis",
    "Luis Ferroni"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "This article concerns the face enumeration of augmented Bergman complexes of matroids, introduced by Braden, Huh, Matherne, Proudfoot and Wang. We prove that the augmented Bergman complex of any matroid admits a convex ear decomposition and deduce that augmented Bergman complexes are doubly Cohen--Macaulay and that they have top-heavy $h$-vectors. We provide some formulas for computing the $h$-polynomials of these complexes and exhibit examples which show that, in general, they are neither log-concave nor unimodal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-11T13:50:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "augmented bergman complex",
      "convex ear decomposition",
      "face enumeration",
      "article concerns",
      "matroid admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}