Infinite words rich and almost rich in generalized palindromes

Edita Pelantová and Štěpán Starosta

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

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