Infinite words rich and almost rich in generalized palindromes

Authors:
Edita Pelantová;Štìpán Starosta
Affiliations:
Department of Mathematics, FNSPE, Czech Technical University in Prague, Praha 2, Czech Republic;Department of Mathematics, FNSPE, Czech Technical University in Prague, Praha 2, Czech Republic
Venue:
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Year:
2011

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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.