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Geometry and combinatoric of Minkowski–Voronoi 3-dimensional continued fractions

Journal of Number Theory. 2017. Vol. 176. P. 375–419.
Karpenkov O., Ustinov A.

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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Keywords: решеткиLattice geometryтрехмерные цепные дробиMinkowski minimaMinkowski – Voronoi continued fractionминимумы Минковского
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