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arXiv · 1102.4023

Infinite words rich and almost rich in generalized palindromes

Edita Pelantová·Štěpán Starosta
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Abstract

We focus on $\Theta$-rich and almost $\Theta$-rich words over a finite alphabet $\mathcal{A}$, where $\Theta$ is an involutive antimorphism over $\mathcal{A}^*$. We show that any recurrent almost $\Theta$-rich word $\uu$ is an image of a recurrent $\Theta'$-rich word under a suitable morphism, where $\Theta'$ is again an involutive antimorphism. Moreover, if the word $\uu$ is uniformly recurrent, we show that $\Theta'$ can be set to the reversal mapping. We also treat one special case of almost $\Theta$-rich words. We show that every $\Theta$-standard words with seed is an image of an Arnoux-Rauzy word.

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Edita Pelantová, Štěpán Starosta. 2011-02-19. Infinite words rich and almost rich in generalized palindromes. https://arxiv.org/abs/1102.4023

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