In a recent paper with L. Q. Zamboni the authors introduced the class of v -episturmian words, where v is an involutory anti-morphism of the free monoid A~*. In this paper, we introduce and study v-characteristic morphisms, that is, morphisms which map standard episturmian words into standard v-episturmian words. They are a natural extension of standard episturmian morphisms. The main result of the paper is a characterization of these morphisms when they are injective.
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