Hasse diagram
If $(A,\le )$ 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

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$$.

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There is no $z\in A$ such that $$ and $$. (There are no inbetween elements.)
If $$, then in $y$ is drawn higher than $x$. Because of that, the direction of the edges is never indicated in a Hasse diagram.
Example: If $A=\mathcal{P}(\{1,2,3\})$, the power set^{} of $\{1,2,3\}$, and $\le $ is the subset relation^{} $\subseteq $, then Hasse diagram is
$$\text{xymatrix}\mathrm{\&}\{1,2,3\}\mathrm{\&}\{1,2\}\text{ar}\mathrm{@}[ur]\mathrm{\&}\{1,3\}\text{ar}\mathrm{@}[u]\mathrm{\&}\{2,3\}\text{ar}\mathrm{@}[ul]\{1\}\text{ar}\mathrm{@}[u]\text{ar}\mathrm{@}[ur]\mathrm{\&}\{2\}\text{ar}\mathrm{@}[ul]\text{ar}\mathrm{@}[ur]\mathrm{\&}\{3\}\text{ar}\mathrm{@}[ul]\text{ar}\mathrm{@}[u]\mathrm{\&}\mathrm{\varnothing}\text{ar}\mathrm{@}[ul]\text{ar}\mathrm{@}[u]\text{ar}\mathrm{@}[ur]\mathrm{\&}$$ 
Even though $$ (since $\{3\}\subset \{1,2,3\}$), there is no edge directly between them because there are inbetween elements: $\{2,3\}$ and $\{1,3\}$. However, there still remains an indirect path from $\{3\}$ to $\{1,2,3\}$.
Title  Hasse diagram 

Canonical name  HasseDiagram 
Date of creation  20130322 12:15:23 
Last modified on  20130322 12:15:23 
Owner  bbukh (348) 
Last modified by  bbukh (348) 
Numerical id  18 
Author  bbukh (348) 
Entry type  Definition 
Classification  msc 05C90 
Related topic  Poset 
Related topic  PartialOrder 