{
  "id": "1406.3081",
  "version": "v3",
  "published": "2014-06-11T22:23:51.000Z",
  "updated": "2015-03-29T02:03:23.000Z",
  "title": "Integer sequences and k-commuting permutations",
  "authors": [
    "Luis Manuel Rivera"
  ],
  "comment": "20 pages, 8 tables. In the second version some paragraphs and proofs were rewritten. V3 is a revised version, one reference added",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\beta$ be any permutation on $n$ symbols and let $c(k, \\beta)$ be the number of permutations that $k$-commute with $\\beta$. The cycle type of a permutation $\\beta$ is a vector $(c_1, \\dots, c_n)$ such that $\\beta$ has exactly $c_i$ cycles of length $i$ in its disjoint cycle factorization. In this article we obtain formulas for $c(k, \\beta)$, for some cycle types. We also express these formulas in terms of integer sequences as given in \"The On-line Encyclopedia of Integer Sequences\" (OEIS). For some of these sequences we obtain either new interpretations or relationships with sequences in the OEIS database.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-26T20:23:54.000Z",
      "abstract": "Let $\\beta$ be any permutation of $n$ symbols and let $c(k, \\beta)$ be the number of permutations that $k$-commute with $\\beta$. The cycle type of a permutation $\\beta$ is a vector $(c_1, \\dots, c_n)$ that means that $\\beta$ has exactly $c_i$ cycles of length $i$ in its disjoint cycle factorization. It is known that $c(k, \\beta)$ only depends of the cycle type of $\\beta$. In this article we obtain formulas for $c(k, \\beta)$, for some cycle types. Also we express these formulas in terms of integer sequences in \"The On-line Encyclopedia of Integer Sequences\" (OEIS). As an application we obtain some relations between sequences in OEIS or new interpretations for some of these sequences.",
      "comment": "20 pages, 8 tables. In the second version some paragraphs and proofs were rewritten",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-03-29T02:03:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "11B99"
    ],
    "keywords": [
      "integer sequences",
      "k-commuting permutations",
      "cycle type",
      "disjoint cycle factorization",
      "on-line encyclopedia"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3081R"
    }
  }
}