Avoiding 5/4-powers on the alphabet of nonnegative integers

05/06/2020

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by   Eric Rowland, et al.

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We identify the structure of the lexicographically least word avoiding 5/4-powers on the alphabet of nonnegative integers. Specifically, we show that this word has the form p τ(φ(z) φ^2(z) ⋯) where p, z are finite words, φ is a 6-uniform morphism, and τ is a coding. This description yields a recurrence for the ith letter, which we use to prove that the sequence of letters is 6-regular with rank 188. More generally, we prove k-regularity for a sequence satisfying a recurrence of the same type.