# Definition:Support of Permutation

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## Definition

Let $S$ be a set.

Let $f$ be a permutation on $S$.

The **support** of $f$ is the subset of moved elements:

- $\map \supp f = \set {x \in S: \map f x \ne x}$

This article is complete as far as it goes, but it could do with expansion.In particular: Possibly worth considering adding a second definition that the support is the complement of $\Fix f$?You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Expand}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |