  It is known that there are no more Lyndon words of length n than there are
periodic necklaces of same length. This paper considers a similar problem
where, additionally, the necklaces must be without some forbidden factors. This
problem relates to a different context, concerned with the behaviours of
particular discrete dynamical systems, namely, Boolean automata networks. A
formal argument supporting the following idea is provided: addition of cycle
intersections in network structures causes exponential reduction of the
networks' number of attractors.
