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

A combinatorial problem about binary necklaces and attractors of Boolean automata networks