A derangement is a bijection $f : A \rightarrow A$ such that $f(x) \ne x$ for all $x \in A$.
Is there a name for a bijection $f : A \rightarrow A$ that is not a derangement? That is, is there a name for a bijection $f : A \rightarrow A$ where $f(x) = x$ for at least on $x \in A$?
Thanks!