{
  "id": "1702.01321",
  "version": "v1",
  "published": "2017-02-04T18:34:53.000Z",
  "updated": "2017-02-04T18:34:53.000Z",
  "title": "A short note on the order of the Zhang-Liu matrices over arbitrary fields",
  "authors": [
    "Leo Betthauser",
    "Josh Hiller"
  ],
  "comment": "Keywords: Pascal Matrix, cyclic group orders, eigenvectors, binomial coefficients, finite fields",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give necessary and sufficient conditions for the Zhang-Liu matrices to be diagonalizable over arbitrary fields and provide the eigen-decomposition when it is possible. We use this result to calculate the order of these matrices over any arbitrary field. This generalizes a result of the second author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-04T18:34:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B36",
      "20H30"
    ],
    "keywords": [
      "arbitrary field",
      "zhang-liu matrices",
      "short note",
      "second author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}