On the Frequency of Letters in Pure Binary Morphic Sequences

Abstract

It is well-known that the frequency of letters in primitive morphic sequences exists. We show that the frequency of letters exists in pure binary morphic sequences generated by non-primitive morphisms. Therefore, the letter frequency exists in every pure binary morphic sequence. We also show that this is somewhat optimal, in the sense that the result does not hold in the class of general binary morphic sequences. Finally, we give an explicit formula for the frequency of letters.