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 | References | Similar Articles | Additional Information
Abstract: Given the finite partially ordered set 
, 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.
- [1] Kirby A. Baker, A generalization of Sperner’s lemma, J. Combinatorial Theory 6 (1969), 224–225. MR 236070
- [2] Marshall Hall Jr., Combinatorial theory, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0224481
- [3] Emanuel Sperner, Ein Satz über Untermengen einer endlichen Menge, Math. Z. 27 (1928), no. 1, 544–548 (German). MR 1544925, https://doi.org/10.1007/BF01171114
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Additional Information
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
