On diversity of certain T-intersecting families

Abstract

Let [n] = {1, 2, . . . , n} and 2[n] be the set of all subsets of [n]. For a family F ⊆ 2[n], its diversity, denoted by div(F), is defined to be div(F) = min x∈[n] {|F(x)|} , where F(x) = {F ∈ F : x / ∈ F}. Basically, div(F) measures how far F is from a trivial intersecting family, which is called a star. In this paper, we consider a generalization of diversity for t-intersecting family.