On θ-episturmian words

AbstractIn 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 θ of the free monoid A∗. We show that given a recurrent infinite word ω∈AN, if there exists a positive integer K such that for each n≥1 the word ω 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 θ of the free monoid A∗ preserving the set of factors of ω