Sperner Partition Systems

Authors


  • Contract grant sponsor: NSERC Discovery; contract grant number: 250389-06 (P. C. L); Contract grant sponsor: NSERC Discovery; contract grant number: 341214-08 (K. M.).

Abstract

A Spernerk-partition system on a set X is a set of partitions of X into k classes such that the classes of the partitions form a Sperner set system (so no class from a partition is a subset of a class from another partition). These systems were defined by Meagher, Moura, and Stevens in [6] who showed that if inline image, then the largest Sperner k-partition system has size inline image. In this paper, we find bounds on the size of the largest Sperner k-partition system where k does not divide the size of X, specifically, we give upper and lower bounds when inline image, inline image and inline image.

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