PosetHeightAndWidth 2005-02-10 23:33:24 2006-12-31 13:39:50 Definition height width % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Let $P$ be a poset. Then the \emph{width} of $P$ is the cardinality of a largest (maximum cardinality) antichain in $P$ and the \emph{height} of $P$ is the cardinality of a longest (maximum cardinality) chain in $P$.