Abstract
This paper is a summary (without proofs) of the main results in a series of papers by the author and D.J. Kleitman [14] and the author [11, 12, 13] concerning subsets of a finite partially ordered set called Sperner k-families. If P is a finite partially ordered set, a subset A ⊆ P is a k-family if A contains no chains of length k+1 (or, equivalently, if A can be expressed as the union of k 1-families in P). Maximum-sized k-families are called Sperner k-families of P.
Supported in part by ONR N00014-67-A-0204-0063.
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© 1975 Mathematical Centre, Amsterdam
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Greene, C. (1975). Sperner Families and Partitions of A Partially Ordered Set. In: Hall, M., van Lint, J.H. (eds) Combinatorics. NATO Advanced Study Institutes Series, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1826-5_15
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DOI: https://doi.org/10.1007/978-94-010-1826-5_15
Publisher Name: Springer, Dordrecht
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