{
  "id": "1710.05214",
  "version": "v1",
  "published": "2017-10-14T17:24:02.000Z",
  "updated": "2017-10-14T17:24:02.000Z",
  "title": "A closed non-iterative formula for straightening fillings of Young diagrams",
  "authors": [
    "Reuven Hodges"
  ],
  "comment": "19 Pages",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process, due to Alfred Young, that expresses a filling of a Young diagram as a sum of semistandard tableau subject to certain relations. It has been a long-standing open problem to give a non-iterative, closed formula for this straightening process. This paper gives such a formula, as well as a simple combinatorial description of the coefficients that arise. Moreover, an interpretation of these coefficients in terms of paths in a directed graph is provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-14T17:24:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05E10",
      "20C30",
      "20C33"
    ],
    "keywords": [
      "young diagram",
      "closed non-iterative formula",
      "straightening fillings",
      "semistandard tableau subject",
      "simple combinatorial description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}