Chain partitions of ordered sets |
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Authors: | Willem L. Fouché |
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Affiliation: | (1) Department of Mathematics and Applied Mathematics, University of Pretoria, 0002 Pretoria, South Africa |
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Abstract: | For natural numbers s and r and a finite poset P of height h, there exists a finite poset P of height H(s, r, h) such that for an arbitrary r-colouring of the s-chains of P, a monochromatically embedded copy of P can be found in P. A best possible upper bound for H(s, r, h) in terms of the well-known Ramsey numbers is given. |
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Keywords: | 06A07 05D10 |
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