Square root of permutation I have been thinking about square roots of permutations. I realized that the square of cycle of odd length is a cycle with the same length and the square of cycle with even length is multiplication of two cycles of half length.

Can the number of roots of some permutation be found in explicit way? What other facts about these roots are known?
You can find a general formula in the following reference: Jesús Leanos, Rutilo Moreno, and Luis Manuel Rivera-Martınez."On the number of mth roots of permutations." AUSTRALASIAN JOURNAL OF COMBINATORICS 52 (2012): 41-54.
You can find a general formula in the following reference: Jesús Leanos, Rutilo Moreno, and Luis Manuel Rivera-Martınez."On the number of mth roots of permutations." AUSTRALASIAN JOURNAL OF COMBINATORICS 52 (2012): 41-54.