Discusses the group structure of Christoffel matrices and finds determinant relationships in Sturmian sequences, suggesting new insights in number theory.
We discuss certain matrices associated with Christoffel words, and show that they have a group structure. We compute their determinants and show a relationship with the Zolotareff symbol from number theory. We show that the n × n determinants constructed from the factors of length n of a Sturmian sequence form a perfectly clustering word on three letters.
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Reutenauer et al. (2026) studied this question.
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