Maximum antichains: a sufficient condition
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- by Michael J. Klass PDF
- Proc. Amer. Math. Soc. 45 (1974), 28-30 Request permission
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.References
- Kirby A. Baker, A generalization of Sperner’s lemma, J. Combinatorial Theory 6 (1969), 224–225. MR 236070
- Marshall Hall Jr., Combinatorial theory, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0224481
- Emanuel Sperner, Ein Satz über Untermengen einer endlichen Menge, Math. Z. 27 (1928), no. 1, 544–548 (German). MR 1544925, DOI 10.1007/BF01171114
Additional Information
- © Copyright 1974 American Mathematical Society
- 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