A periodicity property of iterated morphisms
Department of Mathematics,
University of Turku, 20014 Turku, Finland; email@example.com
Accepted: 13 September 2006
Suppose ƒ : X* → X* is a morphism and u,v ∈ X*. For every nonnegative integer n, let zn be the longest common prefix of ƒn(u) and ƒn(v), and let un,vn ∈ X* be words such that ƒn(u) = znun and ƒn(v) = znvn. We prove that there is a positive integer q such that for any positive integer p, the prefixes of un (resp. vn) of length p form an ultimately periodic sequence having period q. Further, there is a value of q which works for all words u,v ∈ X*.
Mathematics Subject Classification: 68Q45 / 68R15
Key words: Iterated morphism / periodicity
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