Infinite words rich and almost rich in generalized palindromes

Details Infinite words rich and almost rich in generalized palindromes Infinite words rich and almost rich in generalized palindromes

2011-02-19

arxiv.org/abs/1102.4023v1

Mathematics

Combinatorics

10 pages

Scientific paper

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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