Sperner Partition Systems

  title={Sperner Partition Systems},
  author={P. C. Li and Karen Meagher},
  journal={Journal of Combinatorial Designs},
  • P. C. Li, Karen Meagher
  • Published 20 January 2012
  • Mathematics, Computer Science
  • Journal of Combinatorial Designs
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 |X|=kℓ , then the largest Sperner k‐partition system has size 1k|X|ℓ . In this paper, we find bounds on the size of the largest Sperner k‐partition system where k does not divide the size… 
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