{
  "id": "2406.01166",
  "version": "v1",
  "published": "2024-06-03T10:04:03.000Z",
  "updated": "2024-06-03T10:04:03.000Z",
  "title": "Quasisymmetric expansion of Hall-Littlewood symmetric functions",
  "authors": [
    "Darij Grinberg",
    "Ekaterina A. Vassilieva"
  ],
  "comment": "Extended abstract accepted for FPSAC 2024. Comments are welcome! 12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In our previous works we introduced a $q$-deformation of the generating functions for enriched $P$-partitions. We call the evaluation of this generating functions on labelled chains, the $q$-fundamental quasisymmetric functions. These functions interpolate between Gessel's fundamental ($q=0$) and Stembridge's peak ($q=1$) functions, the natural quasisymmetric expansions of Schur and Schur's $Q$-symmetric functions. In this paper, we show that our $q$-fundamental functions provide a quasisymmetric expansion of Hall-Littlewood $S$-symmetric functions with parameter $t=-q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-03T10:04:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "06A11"
    ],
    "keywords": [
      "hall-littlewood symmetric functions",
      "generating functions",
      "natural quasisymmetric expansions",
      "fundamental quasisymmetric functions",
      "stembridges peak"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}