# Sperner Partition Systems

@article{Li2012SpernerPS,
title={Sperner Partition Systems},
author={P. C. Li and Karen Meagher},
journal={Journal of Combinatorial Designs},
year={2012},
volume={21}
}
• 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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## References

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• Mathematics
Electron. J. Comb.
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This paper proves a higher order generalization of Sperner's Theorem and gives a bound on the cardinality of a Sperners-partition system of an $n$-set for any $k$ and $n$.
Erdos-Ko-Rado theorems for uniform set-partition systems
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A higher order generalization of the Erdős-Ko-Rado theorem is proved for systems of pairwise $t-intersecting uniform$k$-partitions of an$n$-set and it is proved that for large enough, any such system contains at most 1-over-k partitions. INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS • Mathematics • 1961 2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set Generating Function for K-Restricted Jagged Partitions • Mathematics Electron. J. Comb. • 2005 The multiple sum that is constructed is the generating function for the so-called$K$-restricted jagged partitions and the corresponding generalization of the Rogers-Ramunjan identities is displayed, together with a novel combinatorial interpretation. Extending Arcs: An Elementary Proof This paper considers two configuration conditions involving arcs in$\pi and shows via combinatorial means that they are equivalent and is able to obtain embeddability results for arcs, all proofs being elementary.