A Generalization of the Bollobás Set Pairs Inequality - O’Neill, Jason; Verstraete, Jacques (The Electronic Journal of Combinatorics, 2021)
The Bollobás set pairs inequality is a fundamental result in extremal set theory with many applications. In this paper, for n k t 2, we consider a collection of k families A_i: 1 ≤ i k where A_i = { A_i,j [n] : j [n] } so that A_1, i_1 … A_k,i_k eq if and only if there are at least t distinct indices i_1,i_2,…,i_k. Via a natural connection to a hypergraph covering problem, we give bounds on the maximum size β_k,t(n) of the families with ground set [n].