{
  "id": "1804.02761",
  "version": "v2",
  "published": "2018-04-08T21:37:07.000Z",
  "updated": "2019-11-01T10:59:57.000Z",
  "title": "Tamari Lattices for Parabolic Quotients of the Symmetric Group",
  "authors": [
    "Henri Mühle",
    "Nathan Williams"
  ],
  "comment": "26 pages, 5 figures, 5 tables. Final version; added more details. Comments are welcome",
  "categories": [
    "math.CO"
  ],
  "abstract": "We generalize the Tamari lattice by extending the notions of $231$-avoiding permutations, noncrossing set partitions, and nonnesting set partitions to parabolic quotients of the symmetric group $\\mathfrak{S}_{n}$. We show bijectively that these three objects are equinumerous. We show how to extend these constructions to parabolic quotients of any finite Coxeter group. The main ingredient is a certain aligned condition of inversion sets; a concept which can in fact be generalized to any reduced expression of any element in any (not necessarily finite) Coxeter group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-11-01T10:59:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "06A07",
      "52C35"
    ],
    "keywords": [
      "parabolic quotients",
      "tamari lattice",
      "symmetric group",
      "finite coxeter group",
      "noncrossing set partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}