{
  "id": "1902.02705",
  "version": "v1",
  "published": "2019-02-07T16:09:38.000Z",
  "updated": "2019-02-07T16:09:38.000Z",
  "title": "Combinatorial specifications for juxtapositions of permutation classes",
  "authors": [
    "Robert Brignall",
    "Jakub Sliacan"
  ],
  "comment": "22 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that, given a suitable combinatorial specification for a permutation class $\\mathcal{C}$, one can obtain a specification for the juxtaposition (on either side) of $\\mathcal{C}$ with Av(21) or Av(12), and that if the enumeration for $\\mathcal{C}$ is given by a rational or algebraic generating function, so is the enumeration for the juxtaposition. Furthermore this process can be iterated, thereby providing an effective method to enumerate any 'skinny' $k\\times 1$ grid class in which at most one cell is non-monotone, with a guarantee on the nature of the enumeration given the nature of the enumeration of the non-monotone cell.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-07T16:09:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation class",
      "juxtaposition",
      "enumeration",
      "suitable combinatorial specification",
      "grid class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}