Modify the program AllPermutations to count the number of permutations of [math]n[/math] objects that have exactly [math]j[/math] fixed points for [math]j = 0, 1, 2,...,n[/math]. Run your program for [math]n = 2[/math] to 6. Make a conjecture for the relation between the number that have 0 fixed points and the number that have exactly 1 fixed point. A proof of the correct conjecture can be found in Wilf.

Notes