Christoffel words and Markoff triples
Christophe Reutenauer
TL;DR
This paper explores the unique parametrization of Markoff triples using Christoffel words, revealing a novel connection between combinatorial word structures and number theory.
Contribution
It introduces a new correspondence between Christoffel words and Markoff triples, providing a combinatorial framework for understanding their relationship.
Findings
Markoff triples are uniquely associated with Christoffel words
A new parametrization method for Markoff triples is proposed
The connection offers insights into number theory and combinatorics
Abstract
Markoff triples are parametrized uniquely by Christoffel words.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Advanced Combinatorial Mathematics