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partition [2019/03/07 11:31] d.gromada |
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==== Graphical representation on one line ==== | ==== Graphical representation on one line ==== | ||
- | We can represent elements $p\in\Part(k)$, that is, partitions of a set $\{1,\dots,k\}$ as diagrams as follows. Put $k$ points on one line representing the elements of the set $\{1,\dots,k\}$. For each block $V\in p$ connect all the points representing elements of $V$ by a node. | + | We can represent elements $p\in\Pscr(k)$, that is, partitions of a set $\{1,\dots,k\}$ as diagrams as follows. Put $k$ points on one line representing the elements of the set $\{1,\dots,k\}$. For each block $V\in p$ connect all the points representing elements of $V$ by a node. |
For example, consider $k=8$ and a partition $p=\{\{1,2,5\},\{3,6\},\{4\},\{7,8\}\}$. This can be represented by the following diagram | For example, consider $k=8$ and a partition $p=\{\{1,2,5\},\{3,6\},\{4\},\{7,8\}\}$. This can be represented by the following diagram |