{
  "id": "1607.02564",
  "version": "v1",
  "published": "2016-07-09T03:51:51.000Z",
  "updated": "2016-07-09T03:51:51.000Z",
  "title": "A base-$b$ extension of the binomial coefficient",
  "authors": [
    "Tanay Wakhare",
    "Christophe Vignat"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We study the properties of the base-$b$ binomial coefficient defined by Jiu and Vignat, introduced in the context of a digital binomial theorem. After introducing a general summation formula we derive base-$b$ analogues of the Stirling numbers of the second kind, the Fibonacci numbers, and the classical exponential function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-09T03:51:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "binomial coefficient",
      "general summation formula",
      "digital binomial theorem",
      "second kind",
      "fibonacci numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}