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Counting families of mutually intersecting sets. (English) Zbl 1267.05144
Summary: 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
\[ \begin{split} 125532424879405039143639827181122982679752727208\\08010757809032705650591023015520462677475328\end{split} \] (roughly \(1.255\cdot 10^{91}\)), respectively.

MSC:
05C30 Enumeration in graph theory
05C75 Structural characterization of families of graphs
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