{
  "id": "1003.1984",
  "version": "v1",
  "published": "2010-03-09T21:21:52.000Z",
  "updated": "2010-03-09T21:21:52.000Z",
  "title": "On the Polya permanent problem over finite fields",
  "authors": [
    "Gregor Dolinar",
    "Alexander E. Guterman",
    "Bojan Kuzma",
    "Marko Orel"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\FF$ be a finite field of characteristics different from two. We show that no bijective map transforms permanent into determinant when the cardinality of $\\FF$ is sufficiently large. We also give an example of non-bijective map when $\\FF$ is arbitrary and an example of a bijective map when $\\FF$ is infinite which do transform permanent into determinant. The developed technique allows us to estimate the probability of the permanent and the determinant of matrices over finite fields to have a given value. Our results are also true over finite rings without zero divisors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-09T21:21:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A15",
      "15A33"
    ],
    "keywords": [
      "finite field",
      "polya permanent problem",
      "bijective map transforms permanent",
      "determinant",
      "transform permanent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1984D"
    }
  }
}