{
  "id": "1407.6217",
  "version": "v2",
  "published": "2014-07-23T13:56:52.000Z",
  "updated": "2016-03-10T19:50:22.000Z",
  "title": "A natural generalization of Balanced Tableaux",
  "authors": [
    "François Viard"
  ],
  "comment": "This new version cointains several major changes in order to take new results into account",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce the notion of \"type\" of a tableau, that allows us to define new families of tableaux including both balanced and standard Young tableaux. We use these new objects to describe the set of reduced decompositions of any permutation. We then generalize the work of Fomin \\emph{et al.} by giving, among other things, a new proof of the fact that balanced and standard tableaux are equinumerous, and by exhibiting many new families of tableaux having similar combinatorial properties to those of balanced tableaux.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-23T13:56:52.000Z",
      "title": "A natural generalisation of Balanced Tableaux",
      "abstract": "We introduce the notion of \"type\" that allows us to define new families of tableaux, which include both balanced and standard Young tableaux. We use these new objects to describe the set of reduced decompositions of any permutation. Moreover, we generalise the work of Edelman and Greene on balanced tableaux by giving among other things, a new proof of the fact that balanced tableaux and standard Young tableaux are equinumerous.",
      "comment": "24 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-03-10T19:50:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "balanced tableaux",
      "natural generalisation",
      "standard young tableaux",
      "permutation",
      "reduced decompositions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.6217V"
    }
  }
}