{
  "id": "1007.0526",
  "version": "v1",
  "published": "2010-07-04T05:42:31.000Z",
  "updated": "2010-07-04T05:42:31.000Z",
  "title": "Determinants and Compositions of Natural Numbers",
  "authors": [
    "Milan Janjic"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider a particular type of matrices which belong at the same time to the class of Hessenberg and Toeplitz matrices, and whose determinants are equal to the number of a type of compositions of natural numbers. We prove a formula in which the number of weak compositions with a fixed number of zeroes is expressed in terms of the number of compositions without zeroes. Then we find a relationship between weak compositions and coefficients of characteristic polynomials of appropriate matrices. Finally, we prove three explicit formulas for weak compositions of a special kind.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-04T05:42:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "natural numbers",
      "weak compositions",
      "determinants",
      "special kind",
      "toeplitz matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0526J"
    }
  }
}