DC Element | Wert | Sprache |
dc.contributor.author | Bruns, Winfried | |
dc.contributor.author | Gubeladze, Joseph | |
dc.contributor.author | Michalek, Mateusz | |
dc.date.accessioned | 2021-12-23T16:20:15Z | - |
dc.date.available | 2021-12-23T16:20:15Z | - |
dc.date.issued | 2016 | |
dc.identifier.issn | 01795376 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/13384 | - |
dc.description.abstract | We introduce a partial order on the set of all normal polytopes in . This poset is a natural discrete counterpart of the continuum of convex compact sets in , ordered by inclusion, and exhibits a remarkably rich combinatorial structure. We derive various arithmetic bounds on elementary relations in , called quantum jumps. The existence of extremal objects in is a challenge of number theoretical flavor, leading to interesting classes of normal polytopes: minimal, maximal, spherical. Minimal elements in have played a critical role in disproving various covering conjectures for normal polytopes in the 1990s. Here we report on the first examples of maximal elements in and , found by a combination of the developed theory, random generation, and extensive computer search. | |
dc.description.sponsorship | DFGGerman Research Foundation (DFG)European Commission [BR 688/22-1]; NSFNational Science Foundation (NSF) [DMS-1301487]; GNSF [DI/16/5-103/12]; Polish National Science Center [2012/05/D/ST1/01063]; Direct For Mathematical & Physical ScienNational Science Foundation (NSF)NSF - Directorate for Mathematical & Physical Sciences (MPS) [1301487] Funding Source: National Science Foundation; We thank B. van Fraassen for his comments in the early stages of this project. We are grateful to anonymous reviewers for their helpful comments and spotting several inaccuracies. Supported by Grants DFG BR 688/22-1 (Bruns), NSF DMS-1301487 and GNSF DI/16/5-103/12 (Gubeladze), Polish National Science Center Grant No. 2012/05/D/ST1/01063 (Michalek) | |
dc.language.iso | en | |
dc.publisher | SPRINGER | |
dc.relation.ispartof | DISCRETE & COMPUTATIONAL GEOMETRY | |
dc.subject | Computer Science | |
dc.subject | Computer Science, Theory & Methods | |
dc.subject | INTEGER ANALOG | |
dc.subject | Lattice polytope | |
dc.subject | Mathematics | |
dc.subject | Maximal polytope | |
dc.subject | Normal polytope | |
dc.subject | Quantum jump | |
dc.title | Quantum Jumps of Normal Polytopes | |
dc.type | journal article | |
dc.identifier.doi | 10.1007/s00454-016-9773-7 | |
dc.identifier.isi | ISI:000377722100007 | |
dc.description.volume | 56 | |
dc.description.issue | 1 | |
dc.description.startpage | 181 | |
dc.description.endpage | 215 | |
dc.contributor.orcid | 0000-0002-6081-786X | |
dc.contributor.researcherid | I-8701-2019 | |
dc.identifier.eissn | 14320444 | |
dc.publisher.place | 233 SPRING ST, NEW YORK, NY 10013 USA | |
dcterms.isPartOf.abbreviation | Discret. Comput. Geom. | |
dcterms.oaStatus | Green Submitted | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | BrWi827 | - |