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2021 Packing minima and lattice points in convex bodies
Martin Henk, Matthias Schymura, Fei Xue
Mosc. J. Comb. Number Theory 10(1): 25-48 (2021). DOI: 10.2140/moscow.2021.10.25

Abstract

Motivated by long-standing conjectures on the discretization of classical inequalities in the geometry of numbers, we investigate a new set of parameters, which we call packing minima, associated to a convex body K and a lattice Λ. These numbers interpolate between the successive minima of K and the inverse of the successive minima of the polar body of K and can be understood as packing counterparts to the covering minima of Kannan & Lovász (1988).

As our main results, we prove sharp inequalities that relate the volume and the number of lattice points in K to the sequence of packing minima. Moreover, we extend classical transference bounds and discuss a natural class of examples in detail.

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Martin Henk. Matthias Schymura. Fei Xue. "Packing minima and lattice points in convex bodies." Mosc. J. Comb. Number Theory 10 (1) 25 - 48, 2021. https://doi.org/10.2140/moscow.2021.10.25

Information

Received: 8 May 2020; Revised: 21 July 2020; Accepted: 7 August 2020; Published: 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.2140/moscow.2021.10.25

Subjects:
Primary: 52C07
Secondary: 11H06, 52C05

Rights: Copyright © 2021 Mathematical Sciences Publishers

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