{
  "id": "1003.4673",
  "version": "v1",
  "published": "2010-03-24T15:52:56.000Z",
  "updated": "2010-03-24T15:52:56.000Z",
  "title": "Kingman, category and combinatorics",
  "authors": [
    "N. H. Bingham",
    "A. J. Ostaszewski"
  ],
  "comment": "34 pages. To appear in Bingham, N. H., and Goldie, C. M. (eds), Probability and Mathematical Genetics: Papers in Honour of Sir John Kingman. London Math. Soc. Lecture Note Series. Cambridge: Cambridge Univ. Press",
  "categories": [
    "math.CA",
    "math.PR"
  ],
  "abstract": "Kingman's Theorem on skeleton limits---passing from limits as $n\\to \\infty $ along $nh$ ($n\\in \\mathbb{N}$) for enough $h>0$ to limits as $t\\to \\infty $ for $t\\in \\mathbb{R}$---is generalized to a Baire/measurable setting via a topological approach. We explore its affinity with a combinatorial theorem due to Kestelman and to Borwein and Ditor, and another due to Bergelson, Hindman and Weiss. As applications, a theory of `rational' skeletons akin to Kingman's integer skeletons, and more appropriate to a measurable setting, is developed, and two combinatorial results in the spirit of van der Waerden's celebrated theorem on arithmetic progressions are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-24T15:52:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A03"
    ],
    "keywords": [
      "combinatorics",
      "van der waerdens celebrated theorem",
      "kingmans integer skeletons",
      "arithmetic progressions",
      "kingmans theorem"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.4673B"
    }
  }
}