On -episturmian words

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 θ of the free monoid A ∗ . We show that given a recurrent infinite word ω ∈ A N , if there exists a positive integer K such that for each n ≥ 1 the word ω has (1) card A + ( 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 .