A periodic point of a function f : X → X is a point x ∈...

A periodic point of a function f : X → X is a point x ∈ X for which there is a number p (a period) with (f(x))^p = x (f^p denotes the composite (f ◦...◦f) of f with itself p times).

A fixpoint is a periodic point with minimal period p = 1, that is, a point x ∈ X such that f(x) = x.

For X = {1,2,...,n}, count the number of functions f : X → X such that each periodic point is a fixpoint.

Hint: What kind of vertebrate do you get when you apply Joyal's bijection on a function like this?

Expert Solution

Answer:-

A periodic point a function f: X to X is a point x ∈ X for which there is a number p (a period) with (f(x))^p = x (f^p .

Colby Messinger answered 3 days ago

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A periodic point of a function f : X → X is a point x ∈...

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