The lexicographically least square-free word with a given prefix

10/02/2022

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by   Siddharth Berera, et al.

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The lexicographically least square-free infinite word on the alphabet of non-negative integers with a given prefix p is denoted L(p). When p is the empty word, this word was shown by Guay-Paquet and Shallit to be the ruler sequence. For other prefixes, the structure is significantly more complicated. In this paper, we show that L(p) reflects the structure of the ruler sequence for several words p. We provide morphisms that generate L(n) for letters n=1 and n≥3, and L(p) for most families of two-letter words p.