{
  "id": "math/0603655",
  "version": "v1",
  "published": "2006-03-28T14:53:16.000Z",
  "updated": "2006-03-28T14:53:16.000Z",
  "title": "Brunn-Minkowski Inequalities for Contingency Tables and Integer Flows",
  "authors": [
    "Alexander Barvinok"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "Given a non-negative mxn matrix W=(w_ij) and positive integer vectors R=(r_1, >..., r_m) and C=(c_1, ..., c_n), we consider the total weight T(R, C; W) of mxn non-negative integer matrices (contingency tables) D with the row sums r_i, the column sums c_j, and the weight of D=(d_ij) equal to product of w_ij^d_ij. In particular, if W is a 0-1 matrix, T(R, C; W) is the number of integer feasible flows in a bipartite network. We prove a version of the Brunn-Minkowski inequality relating the numbers T(R, C; W) and T(R_k, C_k; W), where (R, C) is a convex combination of (R_k, C_k) for k=1, ..., p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-28T14:53:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "52B12",
      "52B20",
      "52A41"
    ],
    "keywords": [
      "contingency tables",
      "brunn-minkowski inequality",
      "integer flows",
      "mxn non-negative integer matrices",
      "positive integer vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3655B"
    }
  }
}