# Category:Hasse Diagrams

This category contains results about Hasse Diagrams.

Definitions specific to this category can be found in Definitions/Hasse Diagrams.

Let $\left({S, \preceq}\right)$ be an ordered set.

A **Hasse diagram** is a method of representing $\left({S, \preceq}\right)$ as a graph $G$, in which:

- $(3):\quad$ If $x, y \in S: x \preceq y$ then the edge representing $x \preceq y$ is drawn so that $x$ is lower down the page than $y$.
- That is, the edge ascends (usually obliquely) from $x$ to $y$

- $(4):\quad$ If $x \preceq y$ and $y \preceq z$, then as an ordering is transitive it follows that $x \preceq z$.
- But in a
**Hasse diagram**, the relation $x \preceq z$ is not shown. - Transitivity is implicitly expressed by the fact that $z$ is higher up than $x$, and can be reached by tracing a path from $x$ to $z$ completely through ascending edges.

- But in a

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