{
  "id": "2403.19744",
  "version": "v1",
  "published": "2024-03-28T18:00:07.000Z",
  "updated": "2024-03-28T18:00:07.000Z",
  "title": "Equality of skew Schur functions in noncommuting variables",
  "authors": [
    "Emma Yu Jin",
    "Stephanie van Willigenburg"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The question of classifying when two skew Schur functions are equal is a substantial open problem, which remains unsolved for over a century. In 2022, Aliniaeifard, Li and van Willigenburg introduced skew Schur functions in noncommuting variables, $s_{(\\delta,D)}$, where $D$ is a connected skew diagram with $n$ boxes and $\\delta$ is a permutation in the symmetric group $S_n$. In this paper, we combine these two and classify when two skew Schur functions in noncommuting variables are equal: $s_{(\\delta,D)} = s_{(\\tau,T)}$ such that $D\\ne T$ if and only if $D$ is a nonsymmetric ribbon, $T$ is the antipodal rotation of $D$ and $\\overline{\\tau^{-1}\\delta}$ is an explicit bijection between two set partitions determined by $D$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-28T18:00:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05A05",
      "05A18",
      "16T30"
    ],
    "keywords": [
      "skew schur functions",
      "noncommuting variables",
      "substantial open problem",
      "explicit bijection",
      "van willigenburg"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}