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arXiv · 1904.01874

A variant of Ostrowski numeration

Emmanuel Cabanillas
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Abstract

In this article, we propose a variant of the usual Ostrowski $α$-numeration (where $α$ is a real in [0, 1[) that codes integers (positive as well as negative) and reals of [0, 1[ (instead of [--$α$, 1--$α$[), so that for every integer n, n and {n$α$} 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 ({n$α$ -- $β$}) n .

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Emmanuel Cabanillas. 2019-09-12. A variant of Ostrowski numeration. https://arxiv.org/abs/1904.01874

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