Atoms of set systems with a fixed number of pairwise unions
Let \(H\) be a system of \(k\) sets with \(u\) pairwise unions, where \(u= (\begin{smallmatrix} t\\ 2\end{smallmatrix})+ \ell+ 1\) and \(0\leq \ell< t\leq k- 1\). The sharp bounds on the number of atoms \(k+ 2^t+ 2^\ell- t\) (for \(t\leq k- 2\)) and \(2^t+ 2^{\ell+ 1}\) (for \(t\neq k- 1\)) are proved.
scientific article; zbMATH DE number 895996
scientific article