| Issue |
RAIRO-Theor. Inf. Appl.
Volume 60, 2026
|
|
|---|---|---|
| Article Number | 6 | |
| Number of page(s) | 23 | |
| DOI | https://doi.org/10.1051/ita/2026005 | |
| Published online | 25 February 2026 | |
Christoffel matrices and Sturmian determinants
1
Département de mathématiques, Université du Québec à Montréal, Canada
2
School of Computer Science, University of Waterloo,
Waterloo,
Ontario
N2L 3G1,
Canada
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
1
November
2024
Accepted:
25
January
2026
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 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.
Mathematics Subject Classification: 68R15 / 11A15 / 05E16
Key words: Combinatorics on words / Burrows–Wheeler matrix / Christoffel word / perfectly clustering word / determinant / Sturmian sequence / group structure / Zolotareff symbol / determinant / Fibonacci number
© The authors. Published by EDP Sciences, 2026
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