Vertical representation of C{\infty}-words

Details Vertical representation of C{\infty}-words Vertical representation of C{\infty}-words

2012-02-23

arxiv.org/abs/1202.5154v1

Computer Science

Discrete Mathematics

Scientific paper

We present a new framework for studying C{\infty}-words, that are arbitrarily many times differentiable words over the alphabet {\Sigma} = {1,2}. After introducing an equivalence relation on C{\infty}-words, whose classes are called minimal classes and represent all the C{\infty}-words, we define a vertical coding of these words based on a three-letter alphabet, and a set of functions operating over this representation. We show that the minimal classes of C{\infty}-words can be represented on an infinite directed acyclic graph, which, as well as all the functions introduced for the vertical coding, can be defined recursively with no explicit reference to C{\infty}-words. This new representation adequately expresses the combinatorial structure of C{\infty}-words, and brings new perspectives in the study of the Kolakoski word and its factors.

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