Sharpness of some intersection theorems
A theorem of \textit{P. Frankl} and \textit{I. G. Rosenberg} [A finite set intersection theorem, Eur. J. Comb. 2, 127-129 (1981; Zbl 0461.05001)] states: Let \(0\leq \mu_1< p\) be integers and let \({\mathcal F}\) be a family of \(k\)-element subsets of an \(n\)-element set such that \(k\not\equiv \mu_1\pmod p\) and \(|F\cap F'|\equiv \mu_1\pmod p\) for any two distinct members \(F\), \(F'\) of \({\mathcal F}\). Then \(|{\mathcal F}|\leq n\). The authors construct infinite sequences of non-trivial families for which the bound is attained. Some further constructions are given for related inequalities.
scientific article; zbMATH DE number 1538573