Geometry and combinatoric of Minkowski--Voronoi 3-dimesional continued fractions

Oleg Karpenkov; Alexey Ustinov

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arXiv · 1407.0135

Geometry and combinatoric of Minkowski--Voronoi 3-dimesional continued fractions

Oleg Karpenkov·Alexey Ustinov

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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.

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Oleg Karpenkov, Alexey Ustinov. 2017-02-01. Geometry and combinatoric of Minkowski--Voronoi 3-dimesional continued fractions. https://arxiv.org/abs/1407.0135

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