Multisets of Aperiodic Cycles
N.G. de Bruijn, David A. Klarner · SIAM Journal on Algebraic and Discrete Methods · 1982
The basic result is that if A is a finite set then there are exactly $| A |^n $ multisets of aperiodic cycles over A with total length n. This is shown by a counting technique but also by establishing an explicit bijection from these multisets to words over A of length n.