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The 3-Irreducible Partially Ordered Sets

Published online by Cambridge University Press:  20 November 2018

David Kelly
David Kelly*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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Abstract

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The dimension [4] of a partially ordered set (poset) is the minimum number of linear orders whose intersection is the partial ordering of the poset. For a positive integer m, a poset is m-irreducible[10] if it has dimension m and removal of any element lowers its dimension. By the compactness property of finite dimension, every m-irreducible poset is finite and every poset of dimension ≧ m contains an m-irreducible subposet.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 367 - 383
Copyright
Copyright © Canadian Mathematical Society 1977

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