{
  "id": "2407.14099",
  "version": "v1",
  "published": "2024-07-19T08:12:23.000Z",
  "updated": "2024-07-19T08:12:23.000Z",
  "title": "Modified Macdonald polynomials and Mahonian statistics",
  "authors": [
    "Emma Yu Jin",
    "Xiaowei Lin"
  ],
  "comment": "25 Pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We establish an equidistribution between the pairs (inv,maj) and (quinv,maj) on any row-equivalency class $[\\tau]$ where $\\tau$ is a filling of a given Young diagram. In particular if $\\tau$ is a filling of a rectangular diagram, the triples (inv,quinv,maj) and (quinv,inv,maj) have the same distribution over $[\\tau]$. Our main result affirms a conjecture proposed by Ayyer, Mandelshtam and Martin (2021), thus presenting the equivalence between two refined formulas for the modified Macdonald polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-19T08:12:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05A19"
    ],
    "keywords": [
      "modified macdonald polynomials",
      "mahonian statistics",
      "main result affirms",
      "row-equivalency class",
      "rectangular diagram"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}