{
  "id": "0908.2609",
  "version": "v2",
  "published": "2009-08-18T18:29:05.000Z",
  "updated": "2010-01-24T16:55:04.000Z",
  "title": "Laurent polynomials and Eulerian numbers",
  "authors": [
    "Daniel Erman",
    "Gregory G. Smith",
    "Anthony Várilly-Alvarado"
  ],
  "comment": "7 pages; gave a new proof of Lemma 3; made minor corrections and improvements to exposition",
  "journal": "Journal of Combinatorial Theory, Series A 118 (2011) 396-402",
  "doi": "10.1016/j.jcta.2010.02.006",
  "categories": [
    "math.CO",
    "math.AC",
    "math.AG"
  ],
  "abstract": "Duistermaat and van der Kallen show that there is no nontrivial complex Laurent polynomial all of whose powers have a zero constant term. Inspired by this, Sturmfels posed two questions: Do the constant terms of a generic Laurent polynomial form a regular sequence? If so, then what is the degree of the associated zero-dimensional ideal? In this note, we prove that the Eulerian numbers provide the answer to the second question. The proof involves reinterpreting the problem in terms of toric geometry.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-24T16:55:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A10",
      "14N15",
      "14M25"
    ],
    "keywords": [
      "eulerian numbers",
      "nontrivial complex laurent polynomial",
      "generic laurent polynomial form",
      "van der kallen",
      "zero constant term"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2609E"
    }
  }
}