On the number of indecomposable permutations with a given number of cycles
Résumé
A permutation $ a_1a_2\ ldots a_n $ is indecomposable if there does not exist $ p< n $ such that $ a_1a_2\ ldots a_p $ is a permutation of $\{1, 2,\ ldots, p\} $. We consider the probability that a permutation of ${\ mathbb S} _n $ with $ m $ cycles is indecomposable and prove that this probability is monotone non-increasing in $ n $.