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Hasse diagram
If $(A,\leq)$ is a finite poset, then it can be represented by a Hasse diagram, which is a graph whose vertices are elements of $A$ and the edges correspond to the covering relation. More precisely an edge from $x\in A$ to $y\in A$ is present if

$x<y$.

There is no $z\in A$ such that $x<z$ and $z<y$. (There are no inbetween elements.)
If $x<y$, then in $y$ is drawn higher than $x$. Because of that, the direction of the edges is never indicated in a Hasse diagram.
Example: If $A=\mathcal{P}(\{1,2,3\})$, the power set of $\{1,2,3\}$, and $\leq$ is the subset relation $\subseteq$, then Hasse diagram is
$\xymatrix{&\{1,2,3\}&\\ \{1,2\}\ar@{}[ur]&\{1,3\}\ar@{}[u]&\{2,3\}\ar@{}[ul]\\ \{1\}\ar@{}[u]\ar@{}[ur]&\{2\}\ar@{}[ul]\ar@{}[ur]&\{3\}\ar@{}[ul]\ar@{}% [u]\\ &\emptyset\ar@{}[ul]\ar@{}[u]\ar@{}[ur]&}$ 
Related:
Poset, PartialOrder
Type of Math Object:
Definition
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Comments
hmm...
I can't seem to get the diagram to show...
investigating now.
yay!
netscape uploads it ok!!
more yay!
I don't even need to use .eps! I can use \xymatrix instead!