, Volume 1, Issue 4, pp 371–375 | Cite as

A companion to Grillet's Theorem on maximal chains and antichains

  • Denis Higgs


It is shown that ifP is a poset containing noN, then every minimal cutset inP is an antichain, that the converse also holds whenP is finite, and that this converse fails in general.

AMS (MOS) subject classification (1980)


Key words

Poset chain antichain cutset 


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  1. 1.
    P. A. Grillet (1969) Maximal chains and antichains,Fund. Math. 65, 157–167.Google Scholar
  2. 2.
    B. Leclerc and B. Monjardet (1973) Ordres ‘C.A.C.’,Fund. Math. 79, 11–22.Google Scholar
  3. 3.
    I. Rival and N. Zaguia (1985) Antichain cutsets,Order 1, 235–247.Google Scholar

Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • Denis Higgs
    • 1
  1. 1.Pure Mathematics DepartmentUniversity of WaterlooWaterlooCanada

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