Densest packings of typical convex sets are not lattice-like
type: Item
instance of: scholarly article
title: Densest packings of typical convex sets are not lattice-like
zbMATH Open document ID: 0829.52006
DOI: 10.1007/BF02570693
author: Yanyan Li
published in: Discrete \& Computational Geometry
publication date: 1995-08-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131389
review text: The packing density \(\delta(C)\) of a set \(C\) with finite positive Lebesgue measure is defined as the supremum of the densities of all packings of congruent copies of \(C\). The lattice-packing density \(\delta_L (C)\) of \(C\) is the supremum of the densities of all lattice packings of \(C\). The author proves: If \(P\) is a convex polygon which has no parallel sides, then \(\delta_L(P) < \delta (P)\). There is a pleasing discussion of related results (e.g., generalized Dirichlet cells, covering) and open problems.
Mathematics Subject Classification ID: 52C05
Mathematics Subject Classification ID: 52C15
zbMATH DE Number: 778436
zbMATH Keywords: density
zbMATH Keywords: lattice-packing
zbMATH Keywords: Dirichlet cells
MaRDI profile type: Publication
cites work: Q4328182
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OpenAlex ID: W2140252779
description: scientific article; zbMATH DE number 778436