On θθ-episturmian words

In this paper we study a class of infinite words on a finite alphabet AA whose factors are closed under the image of an involutory antimorphism θθ of the free monoid A∗A∗. We show that given a recurrent infinite word ω∈ANω∈AN, if there exists a positive integer KK such that for each n≥1n≥1 the word ωω has (1) cardA+(n−1)KcardA+(n−1)K distinct factors of length nn, and (2) a unique right and a unique left special factor of length nn, then there exists an involutory antimorphism θθ of the free monoid A∗A∗ preserving the set of factors of ωω.