New inequalities for families without k pairwise disjoint members

2018/03/15 by Péter Frankl, Peter Frankl, Andrey Kupavskii
Computer Science · Engineering · Mathematics · #Artificial intelligence #Combinatorics #Computer science #Discrete mathematics #Disjoint sets #Graph theory and applications #Inequality #Limits and Structures in Graph Theory #Mathematical analysis #Mathematics #Pairwise comparison #Partition (number theory) #Sharpening #Statistics #cs.DM #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.1016/j.jcta.2018.01.007

openalex publication_date 2018/03/15 · arxiv created 2018/04/10 · arxiv updated 2018/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
• A simple proof of the Erdös-Chao Ko-Rado theorem
• Two problems on matchings in set families - in the footsteps of Erdős and Kleitman