{
  "id": "1603.01736",
  "version": "v1",
  "published": "2016-03-05T15:40:35.000Z",
  "updated": "2016-03-05T15:40:35.000Z",
  "title": "Some Results on Superpatterns for Preferential Arrangements",
  "authors": [
    "Yonah Biers-Ariel",
    "Yiguang Zhang",
    "Anant Godbole"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A {\\it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results on superpatterns for {\\em preferential arrangements}, including (i) a theorem that demonstrates that a string is a superpattern for all preferential arrangements if and only if it is a superpattern for all permutations; and (ii) a result that is reminiscent of a still unresolved conjecture of Alon on the smallest permutation on $[n]$ that contains all $k$-permutations with high probability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-05T15:40:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D99"
    ],
    "keywords": [
      "preferential arrangements",
      "superpattern",
      "smaller strings",
      "probabilistic results",
      "smallest permutation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160301736B"
    }
  }
}