Definition:Support of Permutation

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.

Also see

• Definition:Fixed Element of Permutation