New inequalities for families without k pairwise disjoint members

TL;DR

This paper establishes optimal inequalities for k-partition-free families and uses them to improve a classical bound on families lacking k pairwise disjoint sets.

Contribution

It introduces new inequalities for k-partition-free families and refines existing bounds on families without k disjoint members.

Findings

Established best possible inequalities for k-partition-free families.

Sharpened classical results on families without k pairwise disjoint members.

Abstract

Some best possible inequalities are established for k-partition-free families (cf. Definition 1) and they are applied to prove a sharpening of a classical result of Kleitman concerning families without k pairwise disjoint members.