{
  "id": "math/9409218",
  "version": "v1",
  "published": "1994-09-17T00:00:00.000Z",
  "updated": "1994-09-17T00:00:00.000Z",
  "title": "The lattice of closure relations of a poset",
  "authors": [
    "Michael Hawrylycz",
    "Victor Reiner"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we show that the set of closure relations on a finite poset P forms a supersolvable lattice, as suggested by Rota. Furthermore this lattice is dually isomorphic to the lattice of closed sets in a convex geometry (in the sense of Edelman and Jamison). We also characterize the modular elements of this lattice and compute its characteristic polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-09-17T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07"
    ],
    "keywords": [
      "closure relations",
      "finite poset",
      "convex geometry",
      "modular elements",
      "characteristic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}