{
  "id": "math/0612076",
  "version": "v1",
  "published": "2006-12-04T01:56:18.000Z",
  "updated": "2006-12-04T01:56:18.000Z",
  "title": "Extension of the Bernoulli and Eulerian Polynomials of Higher Order and Vector Partition Function",
  "authors": [
    "Boris Y. Rubinstein"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Following the ideas of L. Carlitz we introduce a generalization of the Bernoulli and Eulerian polynomials of higher order to vectorial index and argument. These polynomials are used for computation of the vector partition function $W({\\bf s},{\\bf D})$, i.e., a number of integer solutions to a linear system ${\\bf x} \\ge 0, {\\bf D x} = {\\bf s}$. It is shown that $W({\\bf s},{\\bf D})$ can be expressed through the vector Bernoulli polynomials of higher order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-04T01:56:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P81",
      "11B68"
    ],
    "keywords": [
      "vector partition function",
      "higher order",
      "eulerian polynomials",
      "vector bernoulli polynomials",
      "linear system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 735839,
      "adsabs": "2006math.....12076R"
    }
  }
}