{
  "id": "1804.06265",
  "version": "v1",
  "published": "2018-04-17T13:59:53.000Z",
  "updated": "2018-04-17T13:59:53.000Z",
  "title": "Pattern Avoidance of Generalized Permutations",
  "authors": [
    "Zhousheng Mei",
    "Suijie Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study pattern avoidances of generalized permutations and show that the number of all generalized permutations avoiding $\\pi$ is independent of the choice of $\\pi\\in S_3$, which extends the classic results on permutations avoiding $\\pi\\in S_3$. Extending both Dyck path and Riordan path, we introduce the Catalan-Riordan path which turns out to be a combinatorial interpretation of the difference array of Catalan numbers. As applications, we interpret Riordan numbers in two ways, via semistandard Young tableaux of two rows and generalized permutations avoiding $\\pi \\in S_3$. Analogous to Lewis's method, we establish a bijection from generalized permutations to rectangular semistandard Young tableaux which will recover several known results in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-17T13:59:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A17",
      "05A19"
    ],
    "keywords": [
      "pattern avoidance",
      "rectangular semistandard young tableaux",
      "generalized permutations avoiding",
      "interpret riordan numbers",
      "classic results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}