Random permutations with cycle lengths in a given finite set
A. N. Timashov · Discrete Mathematics and Applications · 2008
We consider the class of all permutations of degree n whose cycle lengths are elements of a fixed finite set A ⊂ N such that card A ≥ 2 and gcd. Under the assumption that the permutation X is equiprobably chosen from this class, we obtain a multidimensional local normal theorem for the joint distribution of the numbers of cycles of given sizes in this permutation. The obtained results are utilised and sharpened in the case where X is an equiprobably chosen solution of the equation X r = e , where e is an identity permutation of degree n , r ≥ 2 is a fixed positive integer.