Jonathan Caalim

collaborators

3 papers

math.NT2026

Rotational beta expansions and Schmidt games

Hajime Kaneko, Jonathan Caalim, Nathaniel Nollen

We consider rotational beta expansions in dimensions 1, 2 and 4 and view them as expansions on real numbers, complex numbers, and quaternions, respectively. We give sufficient cond…

math.CO2025

On the monoid of lexicographically minimal extensions

Jonathan Caalim, Yu-ichi Tanaka

A sequence $(e_{i})_{i \leq m}$ of nonnegative integers $e_{i}$ , where $m \in N$ or $m = \infty$ , is called a binomid index if $\sum_{i = n - k + 1}^{n} e_{i} \geq \sum_{i = 1}^{k} e_{i}$ for a…

math.NT2025

An analogue of Solomyak's theorem for periodic Cantor real expansions in alternate bases

Jonathan Caalim, Nathaniel Nollen

In this paper, we consider the positional numeration system, called the Cantor real expansion, on the unit interval $[I^^{3}, I^^{3} + 1]$ , where $I^^{3} \in R$ , with respect to an alter…