Abstract

In this paper we study generalization of the reversal mapping realized by an arbitrary involutory antimorphism Θ . It generalizes the notion of a palindrome into a Θ -palindrome—a word invariant under Θ . For languages closed under Θ we give the relation between Θ -palindromic complexity and factor complexity. We generalize the notion of richness to Θ -richness and we prove analogous characterizations of words that are Θ -rich, especially in the case of set of factors invariant under Θ . A criterion for Θ -richness of Θ -episturmian words is given together with other examples of Θ -rich words.

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