{
  "id": "1410.7356",
  "version": "v1",
  "published": "2014-10-27T19:04:40.000Z",
  "updated": "2014-10-27T19:04:40.000Z",
  "title": "Combinatorial Proofs of Identities Involving Symmetric Matrices",
  "authors": [
    "Samantha Dahlberg"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Brualdi and Ma found a connection between involutions of length $n$ with $k$ descents and symmetric $k \\times k$ matrices with non-negative integer entries summing to $n$ and having no row or column of zeros. From their main theorem they derived two alternating sums by algebraic means and asked for combinatorial proofs. The purpose of this note is to give such demonstrations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-27T19:04:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial proofs",
      "symmetric matrices",
      "identities",
      "algebraic means",
      "main theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.7356D"
    }
  }
}