MathDB

f: A \to A, f(k)\ne g(k) and f(f(f(k))= g(k)$ for k \in A

Source: Austrian Polish 1991 APMC

May 1, 2020

functionfunctionalcompositionalgebra

Problem Statement

For a positive integer

n

denote

A = \{1,2,..., n\}

. Suppose that

g : A\to A

is a fixed function with

g(k) \ne k

and

g(g(k)) = k

for

k \in A

. How many functions

f: A \to A

are there such that

f(k)\ne g(k)

and

f(f(f(k))= g(k)

for

k \in A