Zeckendorf Representations and Mixing Properties of Sequences

Authors

Neil Mañibo, Ateneo de Manila UniversityFollow
Eden Delight Miro, Ateneo de Manila UniversityFollow
Dan Rust
Gwendolyn Tadeo, Ateneo de Manila University

Document Type

Article

Publication Date

12-2020

Abstract

We use generalised Zeckendorf representations of natural numbers to investigate mixing properties of symbolic dynamical systems. The systems we consider consist of bi-infinite sequences associated with so-called random substitutions. We focus on random substitutions associated with the Fibonacci; tribonacci and metallic mean numbers and take advantage of their respective numeration schemes.

Recommended Citation

Mañibo, N., Miro, E. D. P., Rust, D., & Tadeo, G. S. (2020). Zeckendorf representations and mixing properties of sequences. Tsukuba Journal of Mathematics, 44(2), 251–269. https://doi.org/10.21099/tkbjm/20204402251