{
  "id": "2201.08168",
  "version": "v1",
  "published": "2022-01-20T13:35:01.000Z",
  "updated": "2022-01-20T13:35:01.000Z",
  "title": "Pattern-avoidance and Fuss-Catalan numbers",
  "authors": [
    "Per Alexandersson",
    "Samuel Asefa Fufa",
    "Frether Getachew",
    "Dun Qiu"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study a subset of permutations, where entries are restricted to having the same remainder as the index, modulo some integer $k \\geq 2$. We show that when also imposing the classical 132- or 213-avoidance restriction on the permutations, we recover the Fuss--Catalan numbers. Surprisingly, an analogous statement also holds when we impose the mod $k$ restriction on a Catalan family of subexcedant functions. Finally, we completely enumerate all combinations of mod-$k$-alternating permutations, avoiding two patterns of length 3. This is analogous to the systematic study by Simion and Schmidt, of permutations avoiding two patterns of length 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-20T13:35:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A19"
    ],
    "keywords": [
      "fuss-catalan numbers",
      "pattern-avoidance",
      "systematic study",
      "subexcedant functions",
      "restriction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}