Counting Families of Mutually Intersecting Sets

A. E. Brouwer, C. F. Mills, W. H. Mills, A. Verbeek

Abstract


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.

 


Keywords


maximal linked systems; Kneser graph; counting independent sets

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