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arXiv · 2507.15313

On a Generalization of the Christoffel Tree: Epichristoffel Trees

Abhishek Krishnamoorthy·Robinson Thamburaj·Durairaj Gnanaraj Thomas
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Abstract

Sturmian words form a family of one-sided infinite words over a binary alphabet that are obtained as a discretization of a line with an irrational slope starting from the origin. A finite version of this class of words called Christoffel words has been extensively studied for their interesting properties. It is a class of words that has a geometric and an algebraic definition, making it an intriguing topic of study for many mathematicians. Recently, a generalization of Christoffel words for an alphabet with 3 letters or more, called epichristoffel words, using episturmian morphisms has been studied, and many of the properties of Christoffel words have been shown to carry over to epichristoffel words; however, many properties are not shared by them as well. In this paper, we introduce the notion of an epichristoffel tree, which proves to be a useful tool in determining a subclass of epichristoffel words that share an important property of Christoffel words, which is the ability to factorize an epichristoffel word as a product of smaller epichristoffel words. We also use the epichristoffel tree to present some interesting results that help to better understand epichristoffel words.

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Abhishek Krishnamoorthy, Robinson Thamburaj, Durairaj Gnanaraj Thomas. 2025-07-21. On a Generalization of the Christoffel Tree: Epichristoffel Trees. https://doi.org/10.4204/eptcs.422.2

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