A subset A of a poset (P,<P) is an antichainMathworldPlanetmath if no two elements are comparable. That is, if a,bA then aPb and bPa.

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.

Title antichain
Canonical name Antichain
Date of creation 2013-03-22 12:52:25
Last modified on 2013-03-22 12:52:25
Owner Henry (455)
Last modified by Henry (455)
Numerical id 6
Author Henry (455)
Entry type Definition
Classification msc 05C05
Classification msc 03E05
Related topic TreeSetTheoretic
Related topic Aronszajn
Defines antichain
Defines maximal antichain