Let S = {1; 2; 3; 4; 5; 6; 7}

Analytically determine the number of maps f from S to S such that f²⁰⁸⁰(x) = x for every x belonging to S.

Note: The iteration is denoted by the superscript, such that f¹(x) = f(x) and
fⁿ(x) = f(f^n-1(x)) for all n > 1.

(In reply to solution by Charlie)

Why do you say there cannot be cycles of length greater than 7? If you had a 3-cycle and a 4-cycle, the total cycle length would be 12.

Posted by Federico Kereki on 2007-08-17 18:44:22