New bounds on the maximum size of Sperner partition systems

Yanxun Chang, Charles J. Colbourn, Adam Gowty, Daniel Horsley, Junling Zhou

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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.

Original languageEnglish
Article number103165
Number of pages18
JournalEuropean Journal of Combinatorics
Publication statusPublished - Dec 2020

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