{
  "id": "2303.17004",
  "version": "v1",
  "published": "2023-03-29T20:14:26.000Z",
  "updated": "2023-03-29T20:14:26.000Z",
  "title": "%-Immanants and Temperley-Lieb Immanants",
  "authors": [
    "Frank Lu",
    "Kevin Ren",
    "Dawei Shen",
    "Siki Wang"
  ],
  "comment": "42 pages, 11 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we investigate the relationship between Temperley-Lieb immanants, which were introduced by Rhoades and Skandera, and %-immanants, an immanant based on a concept introduced by Chepuri and Sherman-Bennett. Our main result is a classification of when a Temperley-Lieb immanant can be written as a linear combination of %-immanants. This result uses a formula by Rhoades and Skandera to compute Temperley-Lieb immanants in terms of complementary minors. Using this formula, we also derive an explicit expression for the coefficients of a Temperley-Lieb immanant coming from a $321$-, $1324$-avoiding permutation $w$ containing the pattern $2143,$ which we use to derive our main result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-29T20:14:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "05E14"
    ],
    "keywords": [
      "temperley-lieb immanant",
      "main result",
      "linear combination",
      "complementary minors",
      "explicit expression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}