Some remarks on differentiable sequences and recursivity

Jean-Marc Fédou (1) , Gabriele Fici (1)

1 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis

We investigate the recursive structure of differentiable sequences over the alphabet {1, 2}. We derive a recursive formula for the (n + 1)-th symbol of a differentiable sequence, which yields to a new recursive formula for the Kolakoski sequence. Finally, we show that the sequence of absolute differences of consecutive symbols of a differentiable sequence u is a morphic image of the run-length encoding of u.

Mots clés: Kolakoski word; differentiable words; recursivity; combinatorics on words

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Jean-Marc Fédou, Gabriele Fici. Some remarks on differentiable sequences and recursivity. Journal of Integer Sequences, 2010, 13 (3), pp.10.3.2. ⟨hal-00463170v2⟩