Say $f(n)$ is number of bijections in a set of $n$ elements without a fixed point. What would this mean? I know that a bijection means that each element in one set is paired with exactly one element in another set. But what does without a fixed point mean?
[Math] What does it mean for a bijection to have no fixed point
elementary-set-theoryfunctions
Best Answer
A fixed point of a function $f:X\to X$ is an element $x\in X$ such that $f(x)=x$.
For instance, if $X=\{1,2,3\}$, then the function defined by $f(1)=1,f(2)=3,f(3)=2$ has $1$ as a fixed point, while the function $g(1)=2,g(2)=3,g(3)=1$ has no fixed points.