A GENERALIZATION OF THE DISCRETE VERSION OF MINKOWSKI'S FUNDAMENTAL THEOREM

DOI10.1112/S002557931500042XzbMath1354.52017arXiv1412.3315OpenAlexW2247417575MaRDI QIDQ2827908

Bernardo González Merino, Matthias Schymura

Publication date: 21 October 2016

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.3315

zbMATH Keywords

volumeMinkowski's fundamental theorem0-symmetric convex body

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Inequalities and extremum problems involving convexity in convex geometry (52A40) Lattices and convex bodies (number-theoretic aspects) (11H06) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Inverse problems of additive number theory, including sumsets (11P70)

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Cites Work

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• Convexity in cristallographical lattices
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• A discrete analogue for Minkowski’s second theorem on successive minima
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• An upper bound for \(d\)-dimensional difference sets