Distribution of facets of higher-dimensional Klein polyhedra

DOI10.1070/SM8788zbMath1417.11133OpenAlexW2790113026MaRDI QIDQ4568558

A. A. Illarionov

Publication date: 22 June 2018

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm8788

zbMATH Keywords

latticemultidimensional continued fractionKlein polyhedron

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Continued fractions and generalizations (11J70) Metric theory of continued fractions (11K50) Nonconvex bodies (11H16)

Related Items (1)

The statistical properties of 3D Klein polyhedra

Cites Work

• On the asymptotic distribution of integer matrices
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• Higher dimensional continued fractions
• Sails and Hilbert bases
• A multidimensional generalization of Lagrange's theorem on continued fractions
• Interior Klein polyhedra
• On an invariant Möbius measure and the Gauss-Kuzmin face distribution
• On the statistical properties of Klein polyhedra in three-dimensional lattices
• The average number of relative minima of three-dimensional integer lattices of a given determinant
• A-graded algebras and continued fractions
• Constructing multidimensional periodic continued fractions in the sense of Klein
• On a multidimensional generalization of Lagrange's theorem on continued fractions
• Some properties of three-dimensional Klein polyhedra
• A multidimensional generalization of Heilbronn's theorem on the average length of a finite continued fraction
• Sails and norm minima of lattices
• Geometry of continued fractions
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