{
  "id": "2003.12123",
  "version": "v1",
  "published": "2020-03-26T19:34:58.000Z",
  "updated": "2020-03-26T19:34:58.000Z",
  "title": "Robinson-Schensted correspondence for unit interval orders",
  "authors": [
    "Dongkwan Kim",
    "Pavlo Pylyavskyy"
  ],
  "comment": "56 pages, 53 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Stanley-Stembridge conjecture associates a symmetric function to each natural unit interval order $\\mathcal P$. In this paper, we define relations \\`a la Knuth on the symmetric group for each $\\mathcal P$ and conjecture that the associated $\\mathcal P$-Knuth equivalence classes are Schur-positive, refining theorems of Gasharov, Brosnan-Chow, and Guay-Paquet. The resulting equivalence graphs fit into the framework of D graphs studied by Assaf. Furthermore, we conjecture that the Schur expansion is given by column-readings of $\\mathcal P$-tableaux that occur in the equivalence class. We prove these conjectures for $\\mathcal P$ avoiding two specific suborders by introducing $\\mathcal P$-analog of Robinson-Schensted insertion, giving an answer to a long standing question of Chow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-26T19:34:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "robinson-schensted correspondence",
      "natural unit interval order",
      "stanley-stembridge conjecture associates",
      "resulting equivalence graphs fit",
      "knuth equivalence classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}