{
  "id": "0907.2870",
  "version": "v1",
  "published": "2009-07-16T15:34:57.000Z",
  "updated": "2009-07-16T15:34:57.000Z",
  "title": "On the least common multiple of $q$-binomial coefficients",
  "authors": [
    "Victor J. W. Guo"
  ],
  "comment": "5 pages",
  "journal": "Integers 10 (2010), 351--356",
  "doi": "10.1515/INTEG.2010.029",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In this paper, we prove the following identity $$ \\lcm({n\\brack 0}_q,{n\\brack 1}_q,...,{n\\brack n}_q) =\\frac{\\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, $$ where ${n\\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\\frac{1-q^n}{1-q}$. This result is a $q$-analogue of an identity of Farhi [Amer. Math. Monthly, November (2009)].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-16T15:34:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "05A30"
    ],
    "keywords": [
      "binomial coefficient",
      "common multiple"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2870G"
    }
  }
}