ON THE NUMBER OF ABELIAN SQUARE-FREE WORDS ON 4 LETTERS

An Abelian square-free substitution on four letters is exhibited. We d erive that, on a four-letter alphabet, the number of Abelian square-fr ee words of each length grows exponentially, infinite Abelian square-f ree words are uncountable and the monoid of Abelian square-free endomo rphisms is not finitely generated.