{
  "id": "1603.07619",
  "version": "v1",
  "published": "2016-03-23T03:57:08.000Z",
  "updated": "2016-03-23T03:57:08.000Z",
  "title": "The number of direct-sum decompositions of a finite vector space",
  "authors": [
    "David Ellerman"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The theory of q-analogs develops many combinatorial formulas for finite vector spaces over a finite field with q elements--all in analogy with formulas for finite sets (which are the special case of q=1). A direct-sum decomposition of a finite vector space is the vector space analogue of a set partition. This paper develops the formulas for the number of direct-sum decompositions that are the q-analogs of the formulas for: (1) the number of set partitions with a given number partition signature; (2) the number of set partitions of an n-element set with m blocks (the Stirling numbers of the second kind); and (3) for the total number of set partitions of an n-element set (the Bell numbers).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-23T03:57:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A18"
    ],
    "keywords": [
      "finite vector space",
      "direct-sum decomposition",
      "set partition",
      "n-element set",
      "vector space analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160307619E"
    }
  }
}