Isomorphism classes of maximal intersecting uniform families are few (Q2583668)

The author shows that the number of nonextendable intersecting \(k\)-families on a finite set, up to isomorphisms, is bounded by a function of \(k\). This is an easy corollary of the following result of \textit{M. Całczyńska-Karlowicz} [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 12, 87--89 (1964; Zbl 0126.02401)]: if \({\mathcal H}\) is an intersecting \(k\)-family on some set \(S\) then there is \(S'\subseteq S\), \(| S'| \leq f(k)\) such that if \(A\neq B\) are in \({\mathcal H}\) then \(A\cap B\cap S'\neq\emptyset\).