On θ-episturmian words

Authors:
Michelangelo Bucci;Aldo de Luca;Alessandro De Luca;Luca Q. Zamboni
Affiliations:
Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Universití degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy;Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Universití degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy;Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Universití degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy;Université de Lyon, Université Lyon 1, CNRS UMR 5208 Institut Camille Jordan, 43, blvd du 11 novembre 1918, F-69622 Villeurbanne Cedex, France and School of Computer Science, Reykjavik U ...
Venue:
European Journal of Combinatorics
Year:
2009

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Abstract

In this paper we study a class of infinite words on a finite alphabet A whose factors are closed under the image of an involutory antimorphism @q of the free monoid A^*. We show that given a recurrent infinite word @w@?A^N, if there exists a positive integer K such that for each n=1 the word @w has (1) cardA+(n-1)K distinct factors of length n, and (2) a unique right and a unique left special factor of length n, then there exists an involutory antimorphism @q of the free monoid A^* preserving the set of factors of @w.