# Category:Disjoint Permutations

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This category contains results about **Disjoint Permutations**.

Definitions specific to this category can be found in **Definitions/Disjoint Permutations**.

Let $S_n$ denote the symmetric group on $n$ letters.

Let $\pi, \rho \in S_n$ both be permutations on $S_n$.

Then $\pi$ and $\rho$ are **disjoint** if and only if:

- $(1): \quad i \notin \Fix \pi \implies i \in \Fix \rho$
- $(2): \quad i \notin \Fix \rho \implies i \in \Fix \pi$

That is, each element moved by $\pi$ is fixed by $\rho$ and (equivalently) each element moved by $\rho$ is fixed by $\pi$.

That is, if and only if their supports are **disjoint sets**.

## Subcategories

This category has only the following subcategory.

## Pages in category "Disjoint Permutations"

The following 2 pages are in this category, out of 2 total.