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## Lattice Representations of Order Ideals of PosetsJuly 17, 2009

Posted by Martin Camacho in combinatorics.
Tags: , ,
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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