{
  "id": "1106.3653",
  "version": "v1",
  "published": "2011-06-18T14:49:14.000Z",
  "updated": "2011-06-18T14:49:14.000Z",
  "title": "Pattern avoidance by even permutations",
  "authors": [
    "Andrew M. Baxter",
    "Aaron D. Jaggard"
  ],
  "comment": "14 pages, 8 figures, 4 tables. Originally presented at Permutation Patterns 2010",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study questions of even-Wilf-equivalence, the analogue of Wilf-equivalence when attention is restricted to pattern avoidance by permutations in the alternating group. Although some Wilf-equivalence results break when considering even-Wilf-equivalence analogues, we prove that other Wilf-equivalence results continue to hold in the even-Wilf-equivalence setting. In particular, we prove that t(t-1)...321 and (t-1)(t-2)...21t are even-shape-Wilf-equivalent for odd t, paralleling a result (which held for all t) of Backelin, West, and Xin for shape-Wilf-equivalence. This allows us to classify the patterns of length 4, and to partially classify patterns of length 5 and 6. As with transition to involution-Wilf-equivalence, some (but not all) of the classical Wilf-equivalence results are preserved when we make the transition to even-Wilf-equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-18T14:49:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "pattern avoidance",
      "permutations",
      "wilf-equivalence results break",
      "wilf-equivalence results continue",
      "classical wilf-equivalence results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3653B"
    }
  }
}