On different generalizations of episturmian words

  • Authors:

  • Michelangelo Bucci;Aldo de Luca;Alessandro De Luca;Luca Q. Zamboni

  • Affiliations:

  • Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy;Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy;Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy;Department of Mathematics, PO Box 311430, University of North Texas, Denton TX, USA

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2008

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Abstract

In this paper we study some classes of infinite words generalizing episturmian words, and analyse the relations occurring among such classes. In each case, the reversal operator R is replaced by an arbitrary involutory antimorphism @q of the free monoid A^*. In particular, we define the class of @q-words with seed, whose ''standard'' elements (@q-standard words with seed) are constructed by an iterative @q-palindrome closure process, starting from a finite word u"0 called the seed. When the seed is empty, one obtains @q-words; episturmian words are exactly the R-words. One of the main theorems of the paper characterizes @q-words with seed as infinite words closed under @q and having at most one left special factor of each length n=N (where N is some nonnegative integer depending on the word). When N=0 we call such words @q-episturmian. Further results on the structure of @q-episturmian words are proved. In particular, some relationships between @q-words (with or without seed) and @q-episturmian words are shown.