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)


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.


Partial Order Weak Order Maximum Antichain Ferrers Diagram Chain Partition 
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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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