ALMOST RICH WORDS AS MORPHIC IMAGES OF RICH WORDS
Edita Pelantová, Štěpán Starosta · International Journal of Foundations of Computer Science · 2012
We focus on Θ-rich and almost Θ-rich words over a finite alphabet [Formula: see text], where Θ is an involutive antimorphism over [Formula: see text]. 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 also 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.