{
  "id": "1811.01696",
  "version": "v1",
  "published": "2018-11-05T14:07:28.000Z",
  "updated": "2018-11-05T14:07:28.000Z",
  "title": "Hodge-Riemann relations for Potts model partition functions",
  "authors": [
    "Petter Brändén",
    "June Huh"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We prove that the Hessians of nonzero partial derivatives of the (homogenous) multivariate Tutte polynomial of any matroid have exactly one positive eigenvalue on the positive orthant when $0<q\\leq 1$. Consequences are proofs of the strongest conjecture of Mason and negative dependence properties for $q$-state Potts model partition functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-05T14:07:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hodge-riemann relations",
      "state potts model partition functions",
      "nonzero partial derivatives",
      "multivariate tutte polynomial",
      "strongest conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}