{
  "id": "1801.07667",
  "version": "v1",
  "published": "2018-01-23T17:25:51.000Z",
  "updated": "2018-01-23T17:25:51.000Z",
  "title": "Puzzles in $K$-homology of Grassmannians",
  "authors": [
    "Pavlo Pylyavskyy",
    "Jed Yang"
  ],
  "comment": "18 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Knutson, Tao, and Woodward formulated a Littlewood-Richardson rule for the cohomology ring of Grassmannians in terms of puzzles. Vakil and Wheeler-Zinn-Justin have found additional triangular puzzle pieces that allow one to express structure constants for $K$-theory of Grassmannians. Here we introduce two other puzzle pieces of hexagonal shape, each of which gives a Littlewood-Richardson rule for $K$-homology of Grassmannians. We also explore the corresponding eight versions of $K$-theoretic Littlewood-Richardson tableaux.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-23T17:25:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15",
      "14M15",
      "52C20"
    ],
    "keywords": [
      "grassmannians",
      "additional triangular puzzle pieces",
      "littlewood-richardson rule",
      "express structure constants",
      "theoretic littlewood-richardson tableaux"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}