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A proof of Sperner's lemma via Hall's theorem

Published online by Cambridge University Press:  24 October 2008

T. C. Brown
T. C. Brown
Affiliation:
Simon Fraser University
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Extract

Let S be a Sperner set of subsets of {1, 2, …, n}. (That is, for A, B ∈ S, if A ≠ B then A ⊄ B and B ⊄ A.) Then

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 3 , November 1975 , pp. 387
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Hall, P.On representation of subsets. J. London Math. Soc. 10 (1935), 26–30.CrossRefGoogle Scholar
(2)Lubell, D.A short proof of Sperner's lemma J. Combinatorial Theory 1 (1966), 299.CrossRefGoogle Scholar
(3)Sperner, E.Ein Satz über Untermengen einer endlichen Menge. Math. Z. 27 (1928), 544–548.CrossRefGoogle Scholar