{
  "id": "1007.0279",
  "version": "v2",
  "published": "2010-07-02T00:05:34.000Z",
  "updated": "2011-12-03T19:35:26.000Z",
  "title": "Congruence conditions, parcels, and Tutte polynomials of graphs and matroids",
  "authors": [
    "Joseph P. S. Kung"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a matrix and $M(G)$ be the matroid defined by linear dependence on the set $E$ of column vectors of $G.$ Roughly speaking, a parcel is a subset of pairs $(f,g)$ of functions defined on $E$ to an Abelian group $A$ satisfying a coboundary condition (that $f-g$ is a flow over $A$ relative to $G$) and a congruence condition (that the size of the supports of $f$ and $g$ satisfy some congruence condition modulo an integer). We prove several theorems of the form: a linear combination of sizes of parcels, with coefficients roots of unity, equals an evaluation of the Tutte polynomial of $M(G)$ at a point $(\\lambda-1,x-1)$ on the complex hyperbola $(\\lambda - 1)(x-1) = |A|.$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-03T19:35:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35"
    ],
    "keywords": [
      "tutte polynomial",
      "congruence condition modulo",
      "coefficients roots",
      "linear combination",
      "complex hyperbola"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0279K"
    }
  }
}