Order

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

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

  • Denis Higgs
Article

Abstract

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)

06A10 

Key words

Poset chain antichain cutset 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations