Is this definition of the support of a permutation correct: let $\pi\in S_{\Omega}$ for $\Omega$ a finite set, and $S_\Omega$ the set of all permutations (bijections) on $\Omega$. Ie $\pi:\Omega\to\Omega$ and is one to one and onto

$$supp(\pi)=\{a\in\Omega\mid\pi(a)\ne a\}$$ $supp(\pi)$ is called the support of $\pi$

This is what my notes say, but I can't find a matching definition on line.

Wikipedia says: Suppose that $f : X \to \mathbb{R}$ is a real-valued function whose domain is an arbitrary set $X$. The set-theoretic support of $f$, written $supp(f)$, is the set of points in X where f is non-zero

$$supp(f) = \{x\in X \mid f(x)\ne 0\}$$


What you have found in Wikipedia is the support of real valued function. It has nothing to do with the support of a permutation.

The definition that you have given is correct.


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