{
  "id": "1208.1915",
  "version": "v2",
  "published": "2012-08-09T14:03:10.000Z",
  "updated": "2012-08-21T05:57:41.000Z",
  "title": "Ascent sequences and 3-nonnesting set partitions",
  "authors": [
    "Sherry H. F. Yan"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:math/0510676 by other authors",
  "categories": [
    "math.CO"
  ],
  "abstract": "A sequence x=x_1 x_2...x_n $ is said to be an ascent sequence of length $n$ if it satisfies x_1=0 and $0\\leq x_i\\leq asc(x_1x_2...x_{i-1})+1$ for all $2\\leq i\\leq n$, where $asc(x_1x_2... x_{i-1})$ is the number of ascents in the sequence $x_1x_2... x_{i-1}$. Recently, Duncan and Steingr\\'{\\i}msson proposed the conjecture that 210-avoiding ascent sequences of length $n$ are equinumerous with 3-nonnesting set partitions of $\\{1,2,..., n\\}$. In this paper, we confirm this conjecture by showing that 210-avoiding ascent sequences of length $n$ are in bijection with 3-nonnesting set partitions of $\\{1,2,..., n\\}$ via an intermediate structure of growth diagrams for 01-fillings of Ferrers shapes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-21T05:57:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "set partitions",
      "ascent sequences",
      "ferrers shapes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1915Y"
    }
  }
}