{
  "id": "1009.2397",
  "version": "v3",
  "published": "2010-09-13T13:57:56.000Z",
  "updated": "2011-09-05T01:54:27.000Z",
  "title": "Computing the partition function for perfect matchings in a hypergraph",
  "authors": [
    "Alexander Barvinok",
    "Alex Samorodnitsky"
  ],
  "comment": "24 pagers, explicit bounds added",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "Given non-negative weights w_S on the k-subsets S of a km-element set V, we consider the sum of the products w_{S_1} ... w_{S_m} for all partitions V = S_1 cup ... cup S_m into pairwise disjoint k-subsets S_i. When the weights w_S are positive and within a constant factor, fixed in advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial in m factor. In the process, we obtain higher-dimensional versions of the van der Waerden and Bregman-Minc bounds for permanents. We also discuss applications to counting of perfect and nearly perfect matchings in hypergraphs.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-05T01:54:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05C65",
      "05C30",
      "15A15",
      "60C05",
      "82B20"
    ],
    "keywords": [
      "perfect matchings",
      "partition function",
      "hypergraph",
      "simple polynomial time algorithm",
      "van der waerden"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.2397B"
    }
  }
}