{
  "id": "2206.08993",
  "version": "v1",
  "published": "2022-06-17T20:07:49.000Z",
  "updated": "2022-06-17T20:07:49.000Z",
  "title": "A bijection between $K$-Kohnert diagrams and reverse set-valued tableaux",
  "authors": [
    "Jianping Pan",
    "Tianyi Yu"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Lascoux polynomials are $K$-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux ($\\mathsf{RSVT}$) rule for Lascoux polynomials and reverse semistandard Young tableaux ($\\mathsf{RSSYT}$) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with $\\mathsf{RSSYT}$. Ross and Yong introduced $K$-Kohnert diagrams, which are analogues of Kohnert diagrams. They conjectured a $K$-Kohnert diagram rule for Lascoux polynomials. We establish this conjecture by constructing a weight-preserving bijection between $\\mathsf{RSVT}$ and $K$-Kohnert diagrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-17T20:07:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "reverse set-valued tableaux",
      "lascoux polynomials",
      "reverse semistandard young tableaux",
      "simple algorithmic model",
      "kohnert diagram rule"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}