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math.CO2024
Christoffel Matrices and Sturmian Determinants
Christophe Reutenauer, Jeffrey Shallit
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 Zolotare…
math.CO2024
Characterizations of Perfectly Clustering Words
Mélodie Lapointe, Christophe Reutenauer
Perfectly clustering words are one of many possible generalizations of Christoffel words. In this article, we propose a factorization of a perfectly clustering word on a letter…
math.CO2024
A Symmetry Property of Christoffel Words
Yan Lanciault, Christophe Reutenauer
Motivated by the theory of trapezoidal words, whose sequences of cardinality of factors by length are symmetric, we introduce a bivariate variant of this symmetry. We show that thi…