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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.


References [Enhancements On Off] (What's this?)

  • [1] K. A. Baker, A generalization of Sperner's lemma, J. Combinatorial Theory, 6(1969), 224-225. MR 38 #4368. MR 0236070 (38:4368)
  • [2] M. Hall, Jr., Combinatorial theory, Blaisdell, Waltham, Mass., 1967, p. 45. MR 37 #80. MR 0224481 (37:80)
  • [3] E. Sperner, Ein Satz über Untermengen einer endlichen Menge, Math. Z. 27(1928), 544-548. MR 1544925

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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

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