{
  "id": "1608.02530",
  "version": "v1",
  "published": "2016-08-08T17:49:40.000Z",
  "updated": "2016-08-08T17:49:40.000Z",
  "title": "Border Ranks of Monomials",
  "authors": [
    "Luke Oeding"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Young flattenings, introduced by Landsberg and Ottaviani, give determinantal equations for secant varieties and provide lower bounds for border ranks of tensors. We find special monomial-optimal Young flattenings that provide the best possible lower bound for all monomials up to degree 6. For degree 7 and higher these flattenings no longer suffice for all monomials. To overcome this problem we introduce partial Young flattenings and use them to give a lower bound on the border rank of monomials which agrees with Landsberg and Teitler's upper bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-08T17:49:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M12",
      "15A69"
    ],
    "keywords": [
      "border rank",
      "lower bound",
      "special monomial-optimal young flattenings",
      "teitlers upper bound",
      "partial young flattenings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}