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On a group theoretic generalization of the Morse-Hedlund theorem

2017
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Proceedings of the American Mathematical Society
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In this paper we give a broad unified framework via group actions for constructing complexity functions of infinite words x = x 0 x 1 x 2 · · · ∈ A N with values in a finite set A. Factor complexity, Abelian complexity and cyclic complexity are all particular cases of this general construction. We consider infinite sequences of permutation groups ω = (G n ) n≥1 with each G n ⊆ S n . Associated with every such sequence is a complexity function p ω,x : N → N which counts, for each length n, the

doi:10.1090/proc/13589
fatcat:cghds5ecr5d3jllbi453jw5tka