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On the Number of Maximal Elements in a Partially Ordered Set

Published online by Cambridge University Press:  20 November 2018

John Ginsburg
John Ginsburg*
Affiliation:
The University of Winnipeg Winnipeg, Manitoba Canada R3B 2E9
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Abstract

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Let P be a partially ordered set. For an element x ∊ P, a subset C of P is called a cutset for x in P if every element of C is noncomparable to x and every maximal chain in P meets {x} ∪ C. The following result is established: if every element of P has a cutset having n or fewer elements, then P has at most 2n maximal elements. It follows that, if some element of P covers k elements of P then there is an element x ∊ P such that every cutset for x in P has at least log2k elements.

Keywords

06A10Partially ordered setcutsetmaximal element
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 3 , 01 September 1987 , pp. 351 - 357
Copyright
Copyright © Canadian Mathematical Society 1987

References

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