{
  "id": "1710.03312",
  "version": "v1",
  "published": "2017-10-09T20:57:28.000Z",
  "updated": "2017-10-09T20:57:28.000Z",
  "title": "Tropicalization, symmetric polynomials, and complexity",
  "authors": [
    "Alexander Woo",
    "Alexander Yong"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO",
    "cs.CC"
  ],
  "abstract": "D. Grigoriev-G. Koshevoy recently proved that tropical Schur polynomials have (at worst) polynomial tropical semiring complexity. They also conjectured tropical skew Schur polynomials have at least exponential complexity; we establish a polynomial complexity upper bound. Our proof uses results about (stable) Schubert polynomials, due to R. P. Stanley and S. Billey-W. Jockusch-R. P. Stanley, together with a sufficient condition for polynomial complexity that is connected to the saturated Newton polytope property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-09T20:57:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric polynomials",
      "polynomial complexity upper bound",
      "tropicalization",
      "conjectured tropical skew schur polynomials",
      "saturated newton polytope property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}