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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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