On the structures of canonical radix expansions in different bases

Abstract Various methods can be employed to formulate number expansions. One of the most intuitive approaches involves the consideration of a lattice, a linear operator acting on it (as the base), and a finite digit set describing the expansions. This study focuses on two-dimensional lattices and bases utilising canonical digit sets. The paper’s main results show (1) how drastically the periodic structure of the expansions changes with the basis change, and (2) how the number system property changes. Efficient algorithmic methods extend the theoretical results.