{
  "id": "2109.02343",
  "version": "v1",
  "published": "2021-09-06T10:32:00.000Z",
  "updated": "2021-09-06T10:32:00.000Z",
  "title": "On the homeomorphism and homotopy type of complexes of multichains",
  "authors": [
    "Shaheen Nazir",
    "Volkmar Welker"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we define and study for a finite partially ordered set P a class of simplicial complexes on the set P_r of r-element multichains from P. The simplicial complexes depend on a strictly monotone function from [r] to [2r]. We show that there exactly 2^r such functions which yield subdivisions of the order complex of P of which 2^{r-1} are pairwise different. Within this class are for example the order complexes of the interval and the zig-zag poset of P and the rth edgewise subdivision of the order complex of P. We also exhibit a large subclass for which our simplicial complexes are order complexes and homotopy equivalent to the order complex of P.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-06T10:32:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "52B99"
    ],
    "keywords": [
      "order complex",
      "homotopy type",
      "simplicial complexes",
      "homeomorphism",
      "zig-zag poset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}