Balanced Fibonacci word rectangles

Apparaît dans la collection : Diophantine approximation and transcendence 2025 / Approximation diophantienne et transcendance 2025

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.

Informations sur la vidéo

Date de captation 10/11/2025
Date de publication 26/11/2025
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20403503
Citer cette vidéo 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

Domaine(s)

Bibliographie

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