Journal of Integer Sequences, Vol. 22 (2019), Article 19.8.2

Finite Test Sets for Morphisms That Are Squarefree on Some of Thue's Squarefree Ternary Words

James D. Currie
Department of Mathematics and Statistics
University of Winnipeg
Winnipeg, Manitoba R3B 2E9


Let S be one of {aba, cbc} and {aba, aca}, and let w be an infinite squarefree word over Σ = {a,b,c} with no factor in S. Suppose that f : Σ → T* is a non-erasing morphism. We prove that the word f(w) is squarefree if and only if f is squarefree on factors of w of length 8 or less.

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(Concerned with sequences A010060 A036577.)

Received October 3 2019; revised versions received November 30 2019; December 7 2019. Published in Journal of Integer Sequences, December 9 2019.

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