2 research outputs found

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

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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 pτ(φ(z)φ2(z)⋯ )p \tau(\varphi(z) \varphi^2(z) \cdots) where p,zp, z are finite words, φ\varphi is a 6-uniform morphism, and τ\tau is a coding. This description yields a recurrence for the iith letter, which we use to prove that the sequence of letters is 6-regular with rank 188. More generally, we prove kk-regularity for a sequence satisfying a recurrence of the same type.Comment: 35 pages, 3 figure

    Avoiding 5/4-powers on the alphabet of nonnegative integers (extended abstract)

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    peer reviewedWe identify the structure of the lexicographically least word avoiding 5/4-powers on the alphabet of nonnegative integers
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