{
  "id": "math/0209340",
  "version": "v1",
  "published": "2002-09-25T14:56:57.000Z",
  "updated": "2002-09-25T14:56:57.000Z",
  "title": "On multi-avoidance of generalized patterns",
  "authors": [
    "T. Mansour",
    "S. Kitaev"
  ],
  "comment": "26 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In [Kit1] Kitaev discussed simultaneous avoidance of two 3-patterns with no internal dashes, that is, where the patterns correspond to contiguous subwords in a permutation. In three essentially different cases, the numbers of such $n$-permutations are $2^{n-1}$, the number of involutions in $\\mathcal{S}_n$, and $2E_n$, where $E_n$ is the $n$-th Euler number. In this paper we give recurrence relations for the remaining three essentially different cases. To complete the descriptions in [Kit3] and [KitMans], we consider avoidance of a pattern of the form $x-y-z$ (a classical 3-pattern) and beginning or ending with an increasing or decreasing pattern. Moreover, we generalize this problem: we demand that a permutation must avoid a 3-pattern, begin with a certain pattern and end with a certain pattern simultaneously. We find the number of such permutations in case of avoiding an arbitrary generalized 3-pattern and beginning and ending with increasing or decreasing patterns.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-25T14:56:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized patterns",
      "multi-avoidance",
      "permutation",
      "th euler number",
      "recurrence relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9340M"
    }
  }
}