Collection Diophantine approximation and transcendence 2025 / Approximation diophantienne et transcendance 2025

Organizer(s) Bugeaud, Yann ; Demarco, Laura ; Gaudron, Eric ; Habegger, Philipp

Date(s) 10/11/2025 - 14/11/2025

linked URL https://conferences.cirm-math.fr/3367.html

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Balanced Fibonacci word rectangles

The infinite Fibonacci word 0100101001 . . . is perhaps the most famous Sturmian word. One of its basic properties is that it is balanced. That is, any two blocks of the same length have either the same sum or their sums are off by 1.In this talk we will consider “Fibonacci word rectangles", i.e., blocks in the corresponding Hankel matrix. Using the software Walnut, we will fully characterise the balanced rectangles. I will also describe the result in terms of distribution modulo 1. Joint work with Jeffrey Shallit.

Information about the video

Date of recording 10/11/2025
Date of publication 26/11/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20403503
Cite this video Vukusic, Ingrid (10/11/2025). Balanced Fibonacci word rectangles. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20403503
URL https://dx.doi.org/10.24350/CIRM.V.20403503

Domain(s)

Bibliography

SHALLIT, Jeffrey et VUKUSIC, Ingrid. Balanced Fibonacci word rectangles, and beyond. arXiv preprint arXiv:2509.25994, 2025. - https://doi.org/10.48550/arXiv.2509.25994