{
  "id": "2203.04590",
  "version": "v1",
  "published": "2022-03-09T09:13:20.000Z",
  "updated": "2022-03-09T09:13:20.000Z",
  "title": "Two conjectures for Macdonald polynomials: The stretching symmetry and Haglund's conjecture",
  "authors": [
    "Seung Jin Lee",
    "Jaeseong Oh",
    "Brendon Rhoades"
  ],
  "comment": "13 pages, comments welcome!",
  "categories": [
    "math.CO"
  ],
  "abstract": "We propose a conjecture which is a symmetry relation for the modified Macdonald polynomials of stretched partitions. We prove the conjecture for one-column or one-row shape in two ways: using the LLT expansion of the modified Macdonald polynomials and using the Garsia--Haiman module. In addition, we prove a conjecture of Haglund concerning multi-$t$-Macdonald polynomials of two rows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-09T09:13:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10"
    ],
    "keywords": [
      "haglunds conjecture",
      "stretching symmetry",
      "modified macdonald polynomials",
      "one-row shape",
      "llt expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}