{
  "id": "1412.5920",
  "version": "v1",
  "published": "2014-12-18T16:14:04.000Z",
  "updated": "2014-12-18T16:14:04.000Z",
  "title": "Connectivity through bounds for the Castelnuovo-Mumford regularity",
  "authors": [
    "Gabriele Balletti"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "We present a simple method to obtain information regarding the connectivity of the 1-skeleta of a wide family of simplicial complexes through bounds for the Castelnuovo-Mumford regularity of their Stanley-Reisner rings. In this way we generalize and unify two results on connectivity: one by Balinsky and Barnette, one by Athanasiadis. In particular, if $\\Delta$ is a simplicial $d$-pseudomanifold, and $s$ is the highest integer such that there is an $s$-dimensional simplex not contained in $\\Delta$, but such that its boundary is, then the 1-skeleton of $\\Delta$ is $\\left\\lceil \\frac{(s+1)d}{s} \\right\\rceil$-connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-18T16:14:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C40",
      "05E40"
    ],
    "keywords": [
      "castelnuovo-mumford regularity",
      "connectivity",
      "dimensional simplex",
      "simple method",
      "highest integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.5920B"
    }
  }
}