Difference between revisions of "Length of a partially ordered set"
From Encyclopedia of Mathematics
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| + | The greatest possible length of a [[chain]] (totally ordered subset) in a [[partially ordered set]] (the length of a finite chain is one less than the number of elements). There exist infinite partially ordered sets of finite length. A partially order set of length zero is a [[trivial order]]. | ||
| − | ==== | + | ====References==== |
| − | + | * George Grätzer, ''General Lattice Theory'', Springer (2003) ISBN 3764369965 | |
Revision as of 20:03, 6 December 2014
2020 Mathematics Subject Classification: Primary: 06A [MSN][ZBL]
The greatest possible length of a chain (totally ordered subset) in a partially ordered set (the length of a finite chain is one less than the number of elements). There exist infinite partially ordered sets of finite length. A partially order set of length zero is a trivial order.
References
- George Grätzer, General Lattice Theory, Springer (2003) ISBN 3764369965
How to Cite This Entry:
Length of a partially ordered set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Length_of_a_partially_ordered_set&oldid=12809
Length of a partially ordered set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Length_of_a_partially_ordered_set&oldid=12809
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article