Rotational beta expansions and Schmidt games

Hajime Kaneko; Jonathan Caalim; Nathaniel Nollen

Rotational beta expansions and Schmidt games

Number Theory 2025-06-17 v2

Authors: Hajime Kaneko , Jonathan Caalim , Nathaniel Nollen

Abstract

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 conditions on the parameters $\alpha, \beta \in (0,1)$ so that particular cylinder sets arising from the expansions are winning or losing Schmidt $(\alpha,\beta)$ -game.

Keywords

random matrix ensembles combinatorial game theory

Cite

@article{arxiv.2502.04149,
  title  = {Rotational beta expansions and Schmidt games},
  author = {Hajime Kaneko and Jonathan Caalim and Nathaniel Nollen},
  journal= {arXiv preprint arXiv:2502.04149},
  year   = {2025}
}

Comments

32 pages. Revised in accordance with the referee report. In particular, we have corrected the deficiencies in the statement and proof of Theorem 4.1. To appear in Acta Mathematica Hungarica

Rotational beta expansions and Schmidt games

Abstract

Keywords

Cite

Comments

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