{
  "id": "math/0409504",
  "version": "v2",
  "published": "2004-09-27T02:34:45.000Z",
  "updated": "2005-05-12T03:23:24.000Z",
  "title": "Lower Bounds for Real Solutions to Sparse Polynomial Systems",
  "authors": [
    "Evgenia Soprunova",
    "Frank Sottile"
  ],
  "comment": "31 pages. Minor revisions",
  "journal": "Advances in Mathematics, Volume 204, Issue 1, 1 August 2006, 116--151.",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "We show how to construct sparse polynomial systems that have non-trivial lower bounds on their numbers of real solutions. These are unmixed systems associated to certain polytopes. For the order polytope of a poset P this lower bound is the sign-imbalance of P and it holds if all maximal chains of P have length of the same parity. This theory also gives lower bounds in the real Schubert calculus through sagbi degeneration of the Grassmannian to a toric variety, and thus recovers a result of Eremenko and Gabrielov.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-05-12T03:23:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "06A07",
      "52B20"
    ],
    "keywords": [
      "real solutions",
      "construct sparse polynomial systems",
      "non-trivial lower bounds",
      "real schubert calculus",
      "maximal chains"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9504S"
    }
  }
}