an:06171923
Zbl 1267.05144
Brouwer, A. E.; Mills, C. F.; Mills, W. H.; Verbeek, A.
Counting families of mutually intersecting sets
EN
Electron. J. Comb. 20, No. 2, Research Paper P8, 8 p. (2013).
00318595
2013
j
05C30 05C75
maximal linked systems; Kneser graph; counting independent sets
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
\[
\begin{multlined}
125532424879405039143639827181122982679752727208\\08010757809032705650591023015520462677475328\end{multlined}
\]
(roughly \(1.255\cdot 10^{91}\)), respectively.