Generating indecomposable permutations

Abstract

An indecomposable permutation π on [ n ] is one such that π ( [ m ] ) = [ m ] for no m < n . We consider indecomposable permutations and give a new, inclusive enumerative recurrence for them. This recurrence allows us to generate all indecomposable permutations of length n in transposition Gray code order, in constant amortized time (CAT). We also present a CAT generation algorithm for indecomposable permutations which is based on the Johnson–Trotter algorithm for generating all permutations of length n. The question of whether or not there exists an adjacent transposition Gray code for indecomposable permutations remains open.