Cycle Decomposition by Disjoint Transpositions

Abstract We investigate in this paper the cycle structures induced on cyclic permutations by disjoint transpositions or, equivalently, the decomposition of a statecycle by interchanging the successors of disjoint state pairs. In both cases we relate the number of resulting cycles to a binary matrix which in a simple manner describes the interaction of the modifications. A possible application to an outstanding problem in shift-register cycle structures is described.