Counting families of mutually intersecting sets (Q1953483)

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.