2019/04/03 by Cabanillas, Emmanuel
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1904.01874
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 nα 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 -- β) n .