antichainAntichain2002-07-26 20:44:492002-08-18 18:32:08Definitionantichainmaximal antichain% this is the default PlanetMath preamble. as your knowledge
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%\PMlinkescapeword{theory}A subset $A$ of a poset $(P,<_P)$ is an \emph{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 \emph{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.