Balanced rectangles over Sturmian words and minimal discrepancy intervals
Abstract
We consider $m\times n$ rectangular matrices formed from Sturmian words with slope $α$, and we fully characterise their balance properties in terms of the Ostrowski representations of $m$ and $n$ with respect to $α$. This generalises recent results by Anselmo et al., as well as those by Shallit and the author, where only quadratic irrational slopes were considered. In contrast to the two mentioned papers, the approach in this paper is based on the distribution of $nα\bmod 1$.
Fields of Study & Subjects
semigroups and automata theory
Mathematical Dynamics and Fractals
Quasicrystal Structures and Properties
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 February 2026
- Language
- EN
- Document type
- Preprint