On the conjugates of Christoffel words
Y. Bugeaud, C. Reutenauer
TL;DR
This paper introduces a new parametrization of Christoffel word conjugates using Ostrowski numeration, providing detailed descriptions of their borders and revisiting the Sturmian graph concept.
Contribution
It offers a novel parametrization method for Christoffel conjugates and enhances understanding of their borders and structural properties.
Findings
Explicit characterization of borders of Christoffel conjugates
A new parametrization based on Ostrowski numeration
Revised insights into Sturmian graph structures
Abstract
We introduce a parametrization of the conjugates of Christoffel words based on the integer Ostrowski numeration system. We use it to give a precise description of the borders (prefixes which are also suffixes) of the conjugates of Christoffel words and to revisit the notion of Sturmian graph introduced by Epifanio et al.
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Taxonomy
Topicssemigroups and automata theory · Natural Language Processing Techniques · Authorship Attribution and Profiling