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arXiv · 1904.09157

New results on pseudosquare avoidance

Tim Ng·Pascal Ochem·Narad Rampersad·Jeffrey Shallit
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Abstract

We start by considering binary words containing the minimum possible numbers of squares and antisquares (where an antisquare is a word of the form $x \overline{x}$), and we completely classify which possibilities can occur. We consider avoiding $x p(x)$, where $p$ is any permutation of the underlying alphabet, and $x t(x)$, where $t$ is any transformation of the underlying alphabet. Finally, we prove the existence of an infinite binary word simultaneously avoiding all occurrences of $x h(x)$ for every nonerasing morphism $h$ and all sufficiently large words $x$.

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Tim Ng, Pascal Ochem, Narad Rampersad, Jeffrey Shallit. 2019-04-19. New results on pseudosquare avoidance. https://arxiv.org/abs/1904.09157

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