{
  "id": "1704.08732",
  "version": "v1",
  "published": "2017-04-27T20:13:27.000Z",
  "updated": "2017-04-27T20:13:27.000Z",
  "title": "Splittability and 1-amalgamability of permutation classes",
  "authors": [
    "Vít Jelínek",
    "Michal Opler"
  ],
  "comment": "17 pages, 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A permutation class $C$ is splittable if it is contained in a merge of its two proper subclasses, and it is 1-amalgamable if given two permutations $\\sigma$ and $\\tau$ in $C$, each with a marked element, we can find a permutation $\\pi$ in $C$ containing both $\\sigma$ and $\\tau$ such that the two marked elements coincide. It was previously shown that unsplittability implies 1-amalgamability. We prove that unsplittability and 1-amalgamability are not equivalent properties of permutation classes by showing that the class $Av(1423, 1342)$ is both splittable and 1-amalgamable. Our construction is based on the concept of LR-inflations, which we introduce here and which may be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-27T20:13:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "permutation class",
      "proper subclasses",
      "independent interest",
      "unsplittability implies",
      "equivalent properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}