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

Department of Mathematics and Statistics

University of Winnipeg

Winnipeg, Manitoba R3B 2E9

Canada

**Abstract:**

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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