Some inequalities for partial orders |
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Authors: | E C Milner Z S Wang B Y Li |
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Institution: | (1) Department of Mathematics, The University of Calgary, T2N 1N4 Calgary, Alberta, Canada;(2) Department of Mathematics, Northwestern University, Xian, Shaanxi, People's Republic of China |
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Abstract: | We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval a,b] contains at most maximal chains, if some antichain has cardinality v, and if there are 1 chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ![les](/content/t421m067111n1261/xxlarge10877.gif) 1 v (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).This paper was written while the authors were visitors at the Laboratoire d'algèbre ordinale, Département de Mathématiques, Université Claude Bernard, Lyon 1, France.Research supported by NSERC grant # A5198. |
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Keywords: | 06A10 |
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