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'Poset height and width'
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| Title of object: |
Poset height and width |
| Canonical Name: |
PosetHeightAndWidth |
| Type: |
Definition |
| Created on: |
2005-02-10 23:33:24 |
| Modified on: |
2005-02-10 23:33:24 |
| Classification: |
msc:06A06 |
| Defines: |
height, width |
Revision comment (for changes between this and next version):
| Changes for correction #5857 ('the title should not be capitalized'). |
Preamble:
% 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 |
Content:
| Let $P$ be a poset. Then the \emph{width} of $P$ is the cardinality of a largest antichain in $P$ and the \emph{height} of $P$ is the cardinality of a longest chain in $P$. |
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