Counting Families of Mutually Intersecting Sets

  • A. E. Brouwer
  • C. F. Mills
  • W. H. Mills
  • A. Verbeek
Keywords: maximal linked systems, Kneser graph, counting independent sets


We show that the number of maximal intersecting families on a 9-set equals 423295099074735261880, that the number of independent sets of the Kneser graph K(9,4) equals 366996244568643864340, and that the number of intersecting families on an 8-set and on a 9-set is 14704022144627161780744368338695925293142507520 and 12553242487940503914363982718112298267975272720808010757809032705650591023015520462677475328 (roughly 1.255 . 10^91), respectively.


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