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On saturated k-Sperner systems

Abstract:

Given a set X, a collection F ⊆ P(X) is said to be k-Sperner if it does not contain a chain of length k + 1 under set inclusion and it is saturated if it is maximal with respect to this property. Gerbner et al. [11] conjectured that, if |X| is sufficiently large with respect to k, then the minimum size of a saturated k-Sperner system F ⊆ P(X) is 2k-1. We disprove this conjecture by showing that there exists ε > 0 such that for every k and |X| ≥ n0(k) there exists a sa...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Authors


Morrison, N More by this author
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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Publisher:
Electronic Journal of Combinatorics Publisher's website
Journal:
Electronic Journal of Combinatorics Journal website
Volume:
21
Issue:
3
Publication date:
2014-08-13
EISSN:
1077-8926
ISSN:
1077-8926
URN:
uuid:cb6d9e51-b60d-41ee-81a3-9590947daa88
Source identifiers:
485524
Local pid:
pubs:485524

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