A note on reflection-free permutation enumeration

Abstract

Earlier it was shown by the present author [1] that among the classical algorithms for the generation of permutation sequences, only the Trotter-Johnson algorithm [2, 3] has the property that the reflection of any permutation in the first half of the enumeration appears only in the second half. Two permutations are called reflections of each other if one read from left to right is the same as the other read from right to left. Lenstra [4] has discussed the usefulness of this property in certain applications. Recently Ives [5] has produced a series of four permutation algorithms of which two (algorithms c and d ) possess the said property.