News about Semiantichains and Unichain Coverings

  • Bartłomiej Bosek
  • Stefan Felsner
  • Kolja Knauer
  • Grzegorz Matecki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)

Abstract

We study a min-max relation conjectured by Saks and West: For any two posets P and Q the size of a maximum semiantichain and the size of a minimum unichain covering in the product P×Q are equal. As a positive result we state conditions on P and Q that imply the min-max relation. However, we also have an example showing that in general the min-max relation is false. This disproves the Saks-West conjecture.

Keywords

Partial Order Weak Order Maximum Antichain Ferrers Diagram Chain Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bartłomiej Bosek
    • 1
  • Stefan Felsner
    • 2
  • Kolja Knauer
    • 2
  • Grzegorz Matecki
    • 1
  1. 1.Theoretical Computer Science Department Faculty of Mathematics and Computer ScienceJagiellonian UniversityPoland
  2. 2.Diskrete Mathematik Institut für MathematikTechnische Universität BerlinGermany

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