On the sizes of t-intersecting k-chain-free families

József Balogh, William B. Linz, Balázs Patkós

Research output: Contribution to journalArticlepeer-review


A set system F is t-intersecting, if the size of the intersection of every pair of its elements has size at least t. A set system F is k-Sperner, if it does not contain a chain of length k + 1. Our main result is the following: Suppose that k and t are fixed positive integers, where n+t is even and n is large enough. If (Math Presents) is a t-intersecting k-Sperner family, then |F| has size at most the size of the sum of k layers, of sizes (n + t)/2, …, (n + t)/2 + k − 1. This bound is best possible. The case when n + t is odd remains open.

Original languageEnglish (US)
JournalCombinatorial Theory
Issue number2
StatePublished - 2023


  • Extremal set theory
  • Sperner families
  • intersection theorems

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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