More Kolakoski Sequences

Abstract

Our goal in this article is to review the known properties of the mysterious Kolakoski sequence and at the same time look at generalizations of it over arbitrary two letter alphabets. Our primary focus will here be the case where one of the letters is odd while the other is even, since in the other cases the sequences in question can be rewritten as (well-known) primitive substitution sequences. We will look at word and letter frequencies, squares, palindromes and complexity.