{
  "id": "1106.5036",
  "version": "v2",
  "published": "2011-06-24T19:00:52.000Z",
  "updated": "2012-03-26T18:31:55.000Z",
  "title": "Set partitions with no m-nesting",
  "authors": [
    "Marni Mishna",
    "Lily Yen"
  ],
  "journal": "In Ilias S. Kotsireas and Eugene V. Zima, editors, Advances in Combinatorics, pages 249-258. Springer Berlin Heidelberg, 2013",
  "doi": "10.1007/978-3-642-30979-3_13",
  "categories": [
    "math.CO"
  ],
  "abstract": "A partition on [n] has an m-nesting if there exists i_1 < i_2 < ... < i_m < j_m < j_{m-1} < ... < j_1, where i_l and j_l are in the same block for all 1 <= l <= m. We use generating trees to construct the class of partitions with no m-nesting and determine functional equations satisfied by the associated generating functions. We use algebraic kernel method together with a linear operator to describe a coefficient extraction process. This gives rise to enumerative data, and illustrates the increasing complexity of the coefficient formulas as m increases.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-26T18:31:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A18"
    ],
    "keywords": [
      "set partitions",
      "coefficient extraction process",
      "algebraic kernel method",
      "coefficient formulas",
      "determine functional equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.5036M"
    }
  }
}