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A subset $A$ of a poset $(P,<_P)$ is an antichain if no two elements are comparable. That is, if $a,b\in A$ then $a\nless_P b$ and $b\nless_P a$
A maximal antichain of $T$ is one which is maximal.
In particular, if $(P,<_P)$ is a tree then the maximal antichains are exactly those antichains which intersect every branch, and if the tree is splitting then every level is a maximal antichain.
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"antichain" is owned by Henry.
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Cross-references: level, branch, intersect, tree, comparable, poset, subset
There are 16 references to this entry.
This is version 3 of antichain, born on 2002-07-26, modified 2002-08-18.
Object id is 3212, canonical name is Antichain.
Accessed 8406 times total.
Classification:
| AMS MSC: | 05C05 (Combinatorics :: Graph theory :: Trees) | | | 03E05 (Mathematical logic and foundations :: Set theory :: Other combinatorial set theory) |
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Pending Errata and Addenda
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