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A Note on Blockers in Posets

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Abstract

The blocker A* of an antichain A in a finite poset P is the set of elements minimal with the property of having with each member of A a common predecessor. The following is done:

(1) The posets P for which A** = A for all antichains are characterized.

(2) The blocker A* of a symmetric antichain in the partition lattice is characterized.

(3) Connections with the question of finding minimal size blocking sets for certain set families are discussed.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Anders Björner & Axel Hultman

Authors
  1. Anders Björner
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  2. Axel Hultman
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Corresponding authors

Correspondence to Anders Björner or Axel Hultman.

Additional information

AMS Subject Classification: 05C35, 05D05, 06A07.

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Björner, A., Hultman, A. A Note on Blockers in Posets. Ann. Combin. 8, 123–131 (2004). https://doi.org/10.1007/s00026-004-0210-x

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  • DOI: https://doi.org/10.1007/s00026-004-0210-x

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