{
  "id": "1603.08490",
  "version": "v1",
  "published": "2016-03-28T19:22:05.000Z",
  "updated": "2016-03-28T19:22:05.000Z",
  "title": "Genomic Tableaux",
  "authors": [
    "Oliver Pechenik",
    "Alexander Yong"
  ],
  "comment": "30 pages, color figures",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We explain how genomic tableaux [Pechenik-Yong '15] are a semistandard complement to increasing tableaux [Thomas-Yong '09]. From this perspective, one inherits genomic versions of jeu de taquin, Knuth equivalence, infusion and Bender-Knuth involutions, as well as Schur functions from (shifted) semistandard Young tableaux theory. These are applied to obtain new Littlewood-Richardson rules for K-theory Schubert calculus of Grassmannians (after [Buch '02]) and maximal orthogonal Grassmannians (after [Clifford-Thomas-Yong '14], [Buch-Ravikumar '12]). For the unsolved case of Lagrangian Grassmannians, sharp upper and lower bounds using genomic tableaux are conjectured.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-28T19:22:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "genomic tableaux",
      "semistandard young tableaux theory",
      "maximal orthogonal grassmannians",
      "inherits genomic versions",
      "k-theory schubert calculus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}