Locally Optimal 2-Periodic Sphere Packings
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Alexei Andreanov | - |
dc.contributor.author | Yoav Kallus | - |
dc.date.available | 2020-01-31T00:49:57Z | - |
dc.date.created | 2019-12-16 | - |
dc.date.issued | 2020-01 | - |
dc.identifier.issn | 0179-5376 | - |
dc.identifier.uri | https://pr.ibs.re.kr/handle/8788114/6684 | - |
dc.description.abstract | The sphere packing problem is an old puzzle. We consider packings with m spheres in the unit cell (m-periodic packings). For the case m = 1 (lattice packings), Voronoi proved there are finitely many inequivalent local optima and presented an algorithm to enumerate them, and this computation has been implemented in up to d = 8 dimensions. We generalize Voronoi’s method to m > 1 and present a procedure to enumerate all locally optimal 2-periodic sphere packings in any dimension, provided there are finitely many. We implement this computation in d = 3, 4, and 5 and show that no 2-periodic packing surpasses the density of the optimal lattices in these dimensions. A partial enumeration is performed in d = 6. © Springer Science+Business Media, LLC, part of Springer Nature 2019 | - |
dc.language | 영어 | - |
dc.publisher | SPRINGER | - |
dc.title | Locally Optimal 2-Periodic Sphere Packings | - |
dc.type | Article | - |
dc.type.rims | ART | - |
dc.identifier.wosid | 000511699300008 | - |
dc.identifier.scopusid | 2-s2.0-85075456093 | - |
dc.identifier.rimsid | 70805 | - |
dc.contributor.affiliatedAuthor | Alexei Andreanov | - |
dc.identifier.doi | 10.1007/s00454-019-00150-6 | - |
dc.identifier.bibliographicCitation | DISCRETE & COMPUTATIONAL GEOMETRY, v.63, no.1, pp.182 - 208 | - |
dc.relation.isPartOf | DISCRETE & COMPUTATIONAL GEOMETRY | - |
dc.citation.title | DISCRETE & COMPUTATIONAL GEOMETRY | - |
dc.citation.volume | 63 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 182 | - |
dc.citation.endPage | 208 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalWebOfScienceCategory | Computer Science, Theory & Methods | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | PERFECT | - |
dc.subject.keywordAuthor | Sphere packing | - |
dc.subject.keywordAuthor | Periodic point set | - |
dc.subject.keywordAuthor | Quadratic form | - |
dc.subject.keywordAuthor | Ryshkov polyhedron | - |