Abstract
We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval [a,b] contains at most λ maximal chains, if some antichain has cardinality v, and if there are χ1 chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ⩽χ1λv (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).
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Communicated by F. Galvin
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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Milner, E.C., Wang, Z.S. & Li, B.Y. Some inequalities for partial orders. Order 3, 369–382 (1987). https://doi.org/10.1007/BF00340779
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DOI: https://doi.org/10.1007/BF00340779