Abstract
A linear extension [x 1<x2<...<xt] of a finite ordered set P=(P, <) is super greedy if it can be obtained using the following procedure: Choose x 1 to be a minimal element of P; suppose x 1,...,x i have been chosen; define p(x) to be the largest j≤i such that x j<x if such a j exists and 0 otherwise; choose x i+1 to be a minimal element of P-{ x 1,...,x i} which maximizes p. Every finite ordered set P can be represented as the intersection of a family of super greedy linear extensions, called a super greedy realizer of P. The super greedy dimension of P is the minimum cardinality of a super greedy realizer of P. Best possible upper bounds for the super greedy dimension of P are derived in terms of |P-A| and width (P-A), where A is a maximal antichain.
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Communicated by D. Kelly
Research supported in part by NSF grant IPS-80110451.
Research supported in part by ONR grant N00014-85K-0494 and NSERC grants 69-3378, 69-0259, and 69-1325.
Research supported in part by NSF grant DMS-8401281.
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Kierstead, H.A., Trotter, W.T. & Zhou, B. Representing an ordered set as the intersection of super greedy linear extensions. Order 4, 293–311 (1987). https://doi.org/10.1007/BF00337892
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DOI: https://doi.org/10.1007/BF00337892