Relation between powers of factors and recurrence function characterizing Sturmian words

Details Relation between powers of factors and recurrence function characterizing Sturmian words Relation between powers of factors and recurrence function characterizing Sturmian words

2008-09-03

arxiv.org/abs/0809.0603v2

Mathematics

Combinatorics

11 pages

Scientific paper

In this paper we use the relation of the index of an infinite aperiodic word
and its recurrence function to give another characterization of Sturmian words.
As a byproduct, we give a new proof of theorem describing the index of a
Sturmian word in terms of the continued fraction expansion of its slope. This
theorem was independently proved by Carpi and de Luca, and Damanik and Lenz.

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