Geometry and combinatoric of Minkowski--Voronoi 3-dimesional continued fractions
Number Theory
2017-02-02 v3 Metric Geometry
Abstract
In this paper we investigate the combinatorial structure of 3-dimensional Minkowski-Voronoi continued fractions. Our main goal is to prove the asymptotic stability of Minkowski-Voronoi complexes in special two-parametric families of rank-1 lattices. In addition we construct explicitly the complexes for the case of White's rank-1 lattices and provide with a hypothetic description in a more complicated settings.
Keywords
Cite
@article{arxiv.1407.0135,
title = {Geometry and combinatoric of Minkowski--Voronoi 3-dimesional continued fractions},
author = {Oleg Karpenkov and Alexey Ustinov},
journal= {arXiv preprint arXiv:1407.0135},
year = {2017}
}