{
  "id": "2107.09149",
  "version": "v1",
  "published": "2021-07-19T20:51:54.000Z",
  "updated": "2021-07-19T20:51:54.000Z",
  "title": "On the generating function for intervals in Young's lattice",
  "authors": [
    "Faqruddin Azam",
    "Edward Richmond"
  ],
  "comment": "18 pages, 1 table",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study a family of generating functions whose coefficients are polynomials that enumerate partitions in lower order ideals of Young's lattice. Our main result is that this family satisfies a rational recursion and are therefore rational functions. As an application, we calculate the asymptotic behavior of the cardinality of lower order ideals for the ``average\" partition of fixed length and give a homological interpretation of this result in relation to Grassmannians and their Schubert varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-19T20:51:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "14M15"
    ],
    "keywords": [
      "youngs lattice",
      "generating function",
      "lower order ideals",
      "main result",
      "enumerate partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}