Christoffel Matrices and Sturmian Determinants
Christophe Reutenauer, Jeffrey Shallit
TL;DR
This paper explores matrices linked to Christoffel words, revealing their group structure, computing their determinants, and connecting them to the Zolotareff symbol, thus bridging combinatorics, algebra, and number theory.
Contribution
It introduces a novel analysis of Christoffel matrices, establishing their group properties and relating their determinants to number-theoretic symbols.
Findings
Christoffel matrices form a mathematical group.
Determinants of these matrices are explicitly computed.
A relationship between these determinants and the Zolotareff symbol is established.
Abstract
We discuss certain matrices associated with Christoffel words, and show that they have a group structure. We compute their determinants and show a relationship between the Zolotareff symbol from number theory.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Graph theory and applications · Matrix Theory and Algorithms