New bounds on the maximum size of Sperner partition systems

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

Research output: Contribution to journalArticlepeer-review

Abstract

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 (US)
Article number103165
JournalEuropean Journal of Combinatorics
Volume90
DOIs
StatePublished - Dec 2020

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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