{
  "id": "1606.02291",
  "version": "v1",
  "published": "2016-06-07T17:36:21.000Z",
  "updated": "2016-06-07T17:36:21.000Z",
  "title": "On Deposition of the Product of Demazure Atoms and Demazure Characters",
  "authors": [
    "Anna Ying Pun"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of a dominating monomial and an atom, which was an open problem. Furthermore, it provides a combinatorial proof to the key-positivity property of the product of a dominating monomial and a key using skyline fillings, an algebraic proof to the key-positivity property of the product of a Schur function and a key using linear operator and verifies the first open case for the conjecture of key-positivity of the product of two keys using linear operators and polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-07T17:36:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "demazure atoms",
      "demazure characters",
      "linear operator",
      "deposition",
      "key-positivity property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}