{
  "id": "1609.04865",
  "version": "v1",
  "published": "2016-09-15T21:40:32.000Z",
  "updated": "2016-09-15T21:40:32.000Z",
  "title": "The Delta Conjecture at $q=1$",
  "authors": [
    "Marino Romero"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We use a weight-preserving, sign-reversing involution to find a combinatorial expansion of $\\Delta_{e_k} e_n$ at $q=1$ in terms of the elementary symmetric function basis. We then use a weight-preserving bijection to prove the Delta Conjecture at $q=1$. The method of proof provides a variety of structures which can compute the inner product of $\\Delta_{e_k} e_n|_{q=1}$ with any symmetric function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-15T21:40:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05Exx",
      "05E05",
      "05E10"
    ],
    "keywords": [
      "delta conjecture",
      "elementary symmetric function basis",
      "combinatorial expansion",
      "inner product",
      "sign-reversing involution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}