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Lattice Representations of Order Ideals of Posets July 17, 2009

Posted by Martin Camacho in combinatorics.
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4 comments

In this post I’ll talk about the representation of order ideals of posets as distributive lattices. You can get a very good description of posets from Stanley’s Enumerative Combinatorics, Vol 1.

First, a couple definitions:

Definition 1 An order ideal of a poset {P} is a set of elements {I} such that if {x\in I} and {y\le x} then {y\in I}

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