{
  "id": "2201.09452",
  "version": "v1",
  "published": "2022-01-24T04:41:14.000Z",
  "updated": "2022-01-24T04:41:14.000Z",
  "title": "On the support of Grothendieck polynomials",
  "authors": [
    "Karola Mészáros",
    "Linus Setiabrata",
    "Avery St. Dizier"
  ],
  "comment": "15 pages, 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Grothendieck polynomials $\\mathfrak{G}_w$ of permutations $w\\in S_n$ were introduced by Lascoux and Sch\\\"utzenberger in 1982 as a set of distinguished representatives for the K-theoretic classes of Schubert cycles in the K-theory of the flag variety of $\\mathbb{C}^n$. We conjecture that the exponents of nonzero terms of the Grothendieck polynomial $\\mathfrak{G}_w$ form a poset under componentwise comparison that is isomorphic to an induced subposet of $\\mathbb{Z}^n$. When $w\\in S_n$ avoids a certain set of patterns, we conjecturally connect the coefficients of $\\mathfrak{G}_w$ with the M\\\"obius function values of the aforementioned poset with $\\hat{0}$ appended. We prove special cases of our conjectures for Grassmannian and fireworks permutations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-24T04:41:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "grothendieck polynomial",
      "special cases",
      "function values",
      "k-theoretic classes",
      "nonzero terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}