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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Maximum antichains: a sufficient condition


Author: Michael J. Klass
Journal: Proc. Amer. Math. Soc. 45 (1974), 28-30
MSC: Primary 06A10
DOI: https://doi.org/10.1090/S0002-9939-1974-0342444-7
MathSciNet review: 0342444
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Abstract: Given the finite partially ordered set $ (Q, \leq )$, one might wish to know whether a maximal (nonextendible) antichain is a maximum antichain. Our result generalizes a theorem of Baker, which in turn constitutes a generalization of Sperner's lemma.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0342444-7
Keywords: Maximum antichains, Sperner's lemma, partially ordered sets
Article copyright: © Copyright 1974 American Mathematical Society