2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67100A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary generating function for simple permutations and that for all permutations, that the coefficients of this series are not P-recursive, an asymptotic expansion for these coefficients, and a number of congruence results.22 pages, 1 figure, submitted to the Journal of Integer SequencesCombinatorics05A05 (Primary) 05A15, 05A16, 11A0 (Secondary)text