Abstract
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 language | English (US) |
---|---|
Journal | Combinatorial Theory |
Volume | 3 |
Issue number | 2 |
DOIs | |
State | Published - 2023 |
Keywords
- Extremal set theory
- Sperner families
- intersection theorems
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics