English

A variant of Ostrowski numeration

Number Theory 2019-09-13 v2

Abstract

In this article, we propose a variant of the usual Ostrowski α\alpha-numeration (where α\alpha is a real in [0, 1[) that codes integers (positive as well as negative) and reals of [0, 1[ (instead of [--α\alpha, 1--α\alpha[), so that for every integer n, n and {nα\alpha} have the same coding sequence. These coding sequences respect natural lexicographic orders and will be used to prove well known results on order properties of Kronecker sequences ({nα\alpha -- β\beta}) n .

Keywords

Cite

@article{arxiv.1904.01874,
  title  = {A variant of Ostrowski numeration},
  author = {Emmanuel Cabanillas},
  journal= {arXiv preprint arXiv:1904.01874},
  year   = {2019}
}
R2 v1 2026-06-23T08:27:51.634Z