Geodesic
Another Note on Sperner's Lemma
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 255-256

Voir la notice de l'article provenant de la source Cambridge University Press

Let Q be a finite partially ordered (by ≤) set with universal bounds O, I. The height function h of Q is defined by the rule: h(x) is the maximum length of a chain from O to x. Let h(I)=n. Suppose that for each k≥0, there exist positive integers a(k) and b(k) such that all elements of height k (i) are covered by a(k) elements of height k+1; (ii) cover b(k) elements of height k—1. Then we call Q a U-poset. Call a subset S of a partially ordered set an antichain if no two elements of S are comparable. 
Drake, David A. Another Note on Sperner's Lemma. Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 255-256. doi: 10.4153/CMB-1971-045-9
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[1] 1. Baker, K. A., A generalization of Sperner's lemma, J. Combinatorial Theory 6 (1969), 224-225. Google Scholar

[2] 2. Birkhoff, G., Lattice theory, Colloq. Publ. 25, 3rd ed., Amer. Math. Soc, Providence, R.I., 1967. Google Scholar

[3] 3. Lubell, D., A short proof of Sperner's lemma, J. Combinatorial Theory 1 (1966), p. 299. Google Scholar

[4] 4. Ore, O., Theory of graphs, Colloq. Publ. 38, Amer. Math. Soc., Providence, R.I., 1962. Google Scholar

[5] 5. Sperner, E., Ein Satz über Untermengen einer endlichen Menge, Math. Zeitsch. 27 (1928), 544-548. Google Scholar

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