{
  "id": "1505.01996",
  "version": "v1",
  "published": "2015-05-08T11:16:25.000Z",
  "updated": "2015-05-08T11:16:25.000Z",
  "title": "The poset of $s$-labeled partitions of $[n]$",
  "authors": [
    "Natalie Aisbett"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "We define a poset called the poset of $s$-labeled partitions of the $[n]$, denoted $\\Pi_{n}^s$, where $s$ is an integer greater than 0. We show that the order complex of $\\overline{\\Pi}_{n}^s$ has the homotopy type of a wedge of spheres of dimension $(n-2)$ by showing that $\\Pi_{n}^s$ is edge-lexicographic shellable. We then find a recursive expression for the number of spheres, and show that when $s=1$ the number of spheres is equal to the number of complete non-ambiguous trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-08T11:16:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07"
    ],
    "keywords": [
      "labeled partitions",
      "integer greater",
      "order complex",
      "homotopy type",
      "complete non-ambiguous trees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}