The enumeration of simple permutations

M. H. Albert, M. D. Atkinson, M. Klazar

Published 2003-04-15Version 1

A 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.