{
  "id": "1410.2933",
  "version": "v1",
  "published": "2014-10-11T00:52:45.000Z",
  "updated": "2014-10-11T00:52:45.000Z",
  "title": "On a refinement of Wilf-equivalence for permutations",
  "authors": [
    "Huiyun Ge",
    "Sherry H. F. Yan",
    "Yaqiu Zhang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Recently, Dokos et al. conjectured that for all $k, m\\geq 1$, the patterns $ 12\\ldots k(k+m+1)\\ldots (k+2)(k+1) $ and $(m+1)(m+2)\\ldots (k+m+1)m\\ldots 21 $ are $maj$-Wilf-equivalent. In this paper, we confirm this conjecture for all $k\\geq 1$ and $m=1$. In fact, we construct a descent set preserving bijection between $ 12\\ldots k (k-1) $-avoiding permutations and $23\\ldots k1$-avoiding permutations for all $k\\geq 3$. As a corollary, our bijection enables us to settle a conjecture of Gowravaram and Jagadeesan concerning the Wilf-equivalence for permutations with given descent sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-11T00:52:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wilf-equivalence",
      "refinement",
      "descent set preserving bijection",
      "conjecture",
      "avoiding permutations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.2933G"
    }
  }
}