{
  "id": "2502.05618",
  "version": "v1",
  "published": "2025-02-08T15:52:23.000Z",
  "updated": "2025-02-08T15:52:23.000Z",
  "title": "Lowering operators on $K$-$k$-Schur functions and a lowering operator formula for closed $K$-$k$-Schur functions",
  "authors": [
    "Yaozhou Fang",
    "Xing Gao",
    "Li Guo"
  ],
  "comment": "41 pages. Comments welcome",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "This paper gives a systematic study of the lowering operators acting on the $K$-$k$-Schur functions, motivated by the pivotal role played by the operators in the definition and study of Katalan functions. A lowering operator formula for closed $K$-$k$-Schur functions is obtained. As an application, a combinatorial proof is provided to a conjecture on closed $k$-Schur Katalan functions, posed by Blasiak, Morse and Seelinger, and recently proved by Ikeda, Iwao and Naito by a different method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-08T15:52:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10",
      "14N15"
    ],
    "keywords": [
      "schur functions",
      "lowering operator formula",
      "schur katalan functions",
      "pivotal role",
      "combinatorial proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}