{
  "id": "math/0311334",
  "version": "v2",
  "published": "2003-11-19T18:50:15.000Z",
  "updated": "2005-01-29T07:39:23.000Z",
  "title": "Tamari lattices and noncrossing partitions in type B and beyond",
  "authors": [
    "Hugh Thomas"
  ],
  "comment": "19 pages, 5 figures; version 2 replaces some incorrect lemmas and incorporates some other more minor improvements",
  "categories": [
    "math.CO"
  ],
  "abstract": "The usual, or type A_n, Tamari lattice is a partial order on T_n^A, the triangulations of an (n+3)-gon. We define a partial order on T_n^B, the set of centrally symmetric triangulations of a (2n+2)-gon. We show that it is a lattice, and that it shares certain other nice properties of the A_n Tamari lattice, and therefore that it deserves to be considered the B_n Tamari lattice. We define a bijection between T_n^B and the non-crossing partitions of type B_n defined by Reiner. For S any subset of [n], Reiner defined a pseudo-type BD^S_n, to which is associated a subset of the noncrossing partitions of type B_n. We show that the elements of T^B_n which correspond to the noncrossing partitions of type BD^S_n posess a lattice structure induced from their inclusion in T^B_n.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-29T07:39:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15"
    ],
    "keywords": [
      "tamari lattice",
      "noncrossing partitions",
      "partial order",
      "lattice structure",
      "centrally symmetric triangulations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11334T"
    }
  }
}