Universität zu Köln

Dostert, Maria ORCID: 0000-0002-0393-8286, Guzman, Cristobal ORCID: 0000-0002-1498-2055, de Oliveira Filho, Fernando Mario and Vallentin, Frank ORCID: 0000-0002-3205-4607 (2017). New Upper Bounds for the Density of Translative Packings of Three-Dimensional Convex Bodies with Tetrahedral Symmetry. Discret. Comput. Geom., 58 (2). S. 449 - 482. NEW YORK: SPRINGER. ISSN 1432-0444

Full text not available from this repository.

Abstract

In this paper we determine new upper bounds for the maximal density of translative packings of superballs in three dimensions (unit balls for the -norm) and of Platonic and Archimedean solids having tetrahedral symmetry. Thereby, we improve Zong's recent upper bound for the maximal density of translative packings of regular tetrahedra from 0.3840 . . . to 03745 . . ., getting closer to the best known lower bound of 0.3673 . . . We apply the linear programming bound of Cohn and Elkies which originally was designed for the classical problem of densest packings of round spheres. The proofs of our new upper bounds are computational and rigorous. Our main technical contribution is the use of invariant theory of pseudo-reflection groups in polynomial optimization.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Dostert, Maria UNSPECIFIED orcid.org/0000-0002-0393-8286 UNSPECIFIED Guzman, Cristobal UNSPECIFIED orcid.org/0000-0002-1498-2055 UNSPECIFIED de Oliveira Filho, Fernando Mario UNSPECIFIED UNSPECIFIED UNSPECIFIED Vallentin, Frank UNSPECIFIED orcid.org/0000-0002-3205-4607 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-218215
DOI:	10.1007/s00454-017-9882-y
Journal or Publication Title:	Discret. Comput. Geom.
Volume:	58
Number:	2
Page Range:	S. 449 - 482
Date:	2017
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0444
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SEMIDEFINITE PROGRAMS; SUPERBALLS; SPHERES Multiple languages Computer Science, Theory & Methods; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/21821