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Duality for Semiantichains and Unichain Coverings in Products of Special Posets

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Abstract

Saks and West conjectured that for every product of partial orders, the maximum size of a semiantichain equals the minimum number of unichains needed to cover the product. We prove the case where both factors have width 2. We also use the characterization of product graphs that are perfect to prove other special cases, including the case where both factors have height 2. Finally, we make some observations about the case where both factors have dimension 2.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA

    Qi Liu & Douglas B. West

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  1. Qi Liu
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  2. Douglas B. West
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Correspondence to Douglas B. West.

Additional information

Work supported in part by NSA Award No. H98230-06-1-0065.

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Liu, Q., West, D.B. Duality for Semiantichains and Unichain Coverings in Products of Special Posets. Order 25, 359–367 (2008). https://doi.org/10.1007/s11083-008-9099-z

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  • DOI: https://doi.org/10.1007/s11083-008-9099-z

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