{
  "id": "1812.11279",
  "version": "v1",
  "published": "2018-12-29T03:48:33.000Z",
  "updated": "2018-12-29T03:48:33.000Z",
  "title": "Powers of a matrix and combinatorial identities",
  "authors": [
    "James Mc Laughlin",
    "B. Sury"
  ],
  "comment": "9 pages",
  "journal": "INTEGERS: The Electronic Journal of Combinatorial Number Theory 5 (2005), A13, 9 pp",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this article we obtain a general polynomial identity in $k$ variables, where $k\\geq 2$ is an arbitrary positive integer. We use this identity to give a closed-form expression for the entries of the powers of a $k \\times k$ matrix. Finally, we use these results to derive various combinatorial identities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-29T03:48:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19"
    ],
    "keywords": [
      "combinatorial identities",
      "general polynomial identity",
      "arbitrary positive integer",
      "closed-form expression"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}