Periodic character sequences where identifying two characters strictly reduces the period (Q1064070)

Let \(A_ m\) be an m element alphabet, where \(m\geq 2\). It is established that, among all periodic sequences in \(A_ m\), there exist those whose primitive period must reduce under every homomorphic map induced by \(\tau:A_ m\to A_{m-1}\) and that, for \(m\geq 3\), their primitive period is equal to, or greater than \({}_ mC_ 2\cdot PP(_ mC_ 2)\), where PP(k) is the product of the smallest k prime numbers. The problem investigated is a property of degenerate cellular automata in which the number of neighbourhood cells is one. The general case is studied by the authors in SIAM J. Comput. 12, 539-550 (1983; Zbl 0525.68032).