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partition [2019/03/07 11:31]
d.gromada
partition [2021/11/23 11:56] (current)
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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
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