{
  "id": "1907.09165",
  "version": "v1",
  "published": "2019-07-22T07:35:15.000Z",
  "updated": "2019-07-22T07:35:15.000Z",
  "title": "Hyperplanes in Configurations, decompositions, and Pascal Triangle of Configurations",
  "authors": [
    "Krzysztof Prażmowski"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An elegant procedure which characterizes a decomposition of some class of binomial configurations into two other, resembling a definition of Pascal's Triangle, was given in \\cite{gevay}. In essence, this construction was already presented in \\cite{perspect}. We show that such a procedure is a result of fixing in configurations in some class $\\mathcal K$ suitable hyperplanes which both: are in this class, and deleting such a hyperplane results in a configuration in this class. By a way of example we show two more (added to that of \\cite{gevay}) natural classes of such configurations, discuss some other, and propose some open questions that seem also natural in this context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-22T07:35:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B30",
      "51E30",
      "51E20"
    ],
    "keywords": [
      "pascal triangle",
      "decomposition",
      "pascals triangle",
      "binomial configurations",
      "hyperplane results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}