The EKR theorem states that the largest uniform intersecting family consists of all sets containing a given element, that is, the maximal family of diversity 0.

Sep 8, 2017 · Given an intersecting family, its diversity is the number of sets not passing through the most popular element of the ground set. Peter Frankl ...

Given an intersecting family, its diversity is the number of sets not passing through the most popular element of the ground set. Peter Frankl made the ...

Jun 29, 2018 · The diversity γ(F) of F is the number of sets, not containing the element of the largest degree: γ(F) := |F| − ∆(F). The study of intersecting ...

Diversity of uniform intersecting families. Andrey Kupavskii∗. Abstract. A family F ⊂ 2[n] is called intersecting, if any two of its sets intersect. Given an ...

A family f ⊂ 2 [ n ] \mathcal f\subset 2^{[n]} is called {\it intersecting}, if any two of its sets intersect. Given an intersecting family, ...

Given an intersecting family, its diversity is the number of sets not passing through a fixed most popular element of the ground set. Peter Frankl made the ...

Diversity can be viewed as a measure of distance from the 'trivial' maximum-size intersecting family given by the Erdős–Ko–Rado Theorem. Indeed, the diversity ...

21 Citations · A generalization of diversity for intersecting families · Improved bounds on the maximum diversity of intersecting families · Two extremal problems ...

Moreover it also has the largest diversity. We believe that this property is the main reason that causes the resulting uniform family F to have large diversity.