{
  "id": "2401.15887",
  "version": "v1",
  "published": "2024-01-29T04:47:52.000Z",
  "updated": "2024-01-29T04:47:52.000Z",
  "title": "Rational reductions for holonomic sequences",
  "authors": [
    "Rong-Hua Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a holonomic sequence $F(n)$, we characterize rational functions $r(n)$ so that $r(n)F(n)$ can be summable. We provide upper and lower bounds on the degree of the numerator of $r(k)$ and show the denominator of $r(n)$ can be read from annihilators of $F(k)$. This illustration provides the so-called rational reductions which can be used to generate new multi-sum equalities and congruences from known ones.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-29T04:47:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "holonomic sequence",
      "rational reductions",
      "multi-sum equalities",
      "characterize rational functions",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}