{
  "id": "0906.1836",
  "version": "v1",
  "published": "2009-06-10T18:13:12.000Z",
  "updated": "2009-06-10T18:13:12.000Z",
  "title": "Generating functions attached to some infinite matrices",
  "authors": [
    "Paul Monsky"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "Let V be an infinite matrix with rows and columns indexed by the positive integers, and entries in a field F. Suppose that v_{i,j} only depends on i-j and is 0 for |i-j| large. Then V^n is defined for all n, and one has a \"generating function\" G=\\sum a_{1,1}(V^n)z^n. Ira Gessel has shown that G is algebraic over F(z). We extend his result, allowing v_{i,j} for fixed i-j to be eventually periodic in i rather than constant. This result and some variants of it that we prove will have applications to Hilbert-Kunz theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-10T18:13:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generating functions",
      "infinite matrices",
      "hilbert-kunz theory",
      "infinite matrix",
      "ira gessel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.1836M"
    }
  }
}