{
  "id": "1703.03313",
  "version": "v1",
  "published": "2017-03-09T15:57:56.000Z",
  "updated": "2017-03-09T15:57:56.000Z",
  "title": "On realizability of sign patterns by real polynomials",
  "authors": [
    "Vladimir Petrov Kostov"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The classical Descartes' rule of signs limits the number of positive roots of a real polynomial in one variable by the number of sign changes in the sequence of its coefficients. One can ask the question which pairs of nonnegative integers $(p,n)$, chosen in accordance with this rule and with some other natural conditions, can be the pairs of numbers of positive and negative roots of a real polynomial with prescribed signs of the coefficients. The paper solves this problem for degree $8$ polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-09T15:57:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real polynomial",
      "sign patterns",
      "realizability",
      "signs limits",
      "natural conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}