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Main Title: Bounds on the lattice point enumerator via slices and projections
Author(s): Freyer, Ansgar
Henk, Martin
Type: Article
Abstract: Gardner et al. posed the problem to find a discrete analogue of Meyer’s inequality bounding from below the volume of a convex body by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated by this problem, for which we provide a first general bound, we study in a more general context the question of bounding the number of lattice points of a convex body in terms of slices, as well as projections.
Subject(s): lattice point enumerator
Loomis−Whitney inequality
Meyer’s inequality
slicing problem
successive minima
Issue Date: 3-Jun-2021
Date Available: 17-May-2022
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: TU Berlin, Open-Access-Mittel – 2021
Journal Title: Discrete and Computational Geometry
Publisher: Springer Nature
Volume: 67
Publisher DOI: 10.1007/s00454-021-00310-7
Page Start: 895
Page End: 918
EISSN: 1432-0444
ISSN: 0179-5376
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Diskrete Mathematik / Geometrie
Appears in Collections:Technische Universität Berlin » Publications

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