An (n,k)-Sperner partition system is a collection of partitions of some n-set, each into k nonempty classes, such that no class of any partition is a subset of a class of any other. The maximum number of partitions in an (n,k)-Sperner partition system is denoted SP(n,k). In this paper we introduce a new construction for Sperner partition systems and use it to asymptotically determine SP(n,k) in many cases as [Formula presented] becomes large. We also give a slightly improved upper bound for SP(n,k) and exhibit an infinite family of parameter sets (n,k) for which this bound is tight.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics