{
  "id": "1306.2930",
  "version": "v4",
  "published": "2013-06-12T19:19:05.000Z",
  "updated": "2015-08-01T17:41:23.000Z",
  "title": "Another proof of Wilmes' conjecture",
  "authors": [
    "Sam Hopkins"
  ],
  "comment": "8 pages, 1 figure. v2: added reference to a recent preprint of Mohammadi and Shokrieh. v3: to appear in Discrete Math, v4: minor typo corrected",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present a new proof of the monomial case of Wilmes' conjecture, which gives a formula for the coarsely-graded Betti numbers of the G-parking function ideal in terms of maximal parking functions of contractions of G. Our proof is via poset topology and relies on a theorem of Gasharov, Peeva, and Welker that connects the Betti numbers of a monomial ideal to the topology of its lcm-lattice.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-01-21T21:55:46.000Z",
      "comment": "8 pages, 1 figure. v2: added reference to a recent preprint of Mohammadi and Shokrieh. v3: to appear in Discrete Math",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-08-01T17:41:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E40",
      "05C25",
      "13D02",
      "06B30"
    ],
    "keywords": [
      "conjecture",
      "monomial case",
      "monomial ideal",
      "poset topology",
      "coarsely-graded betti numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.2930H"
    }
  }
}