dc.contributor.author
Padrol, Arnau
dc.contributor.author
Pfeifle, Julian
dc.date.accessioned
2018-06-08T03:44:42Z
dc.date.available
2016-04-01T10:19:48.816Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/15843
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-20030
dc.description.abstract
We show that every heptagon is a section of a 3-polytope with 6 vertices. This
implies that every n-gon with n≥7 can be obtained as a section of a
(2+⌊n7⌋)-dimensional polytope with at most ⌈6n7⌉ vertices; and provides a
geometric proof of the fact that every nonnegative n×m matrix of rank 3 has
nonnegative rank not larger than ⌈6min(n,m)7⌉. This result has been
independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122,
2014).
en
dc.rights.uri
http://www.combinatorics.org/ojs/index.php/eljc/about/submissions#copyrightNotice
dc.subject
polytope projections and sections
dc.subject
extension complexity
dc.subject
nonnegative rank
dc.subject
nonrealizability
dc.subject
pseudo-line arrangements
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik
dc.title
Polygons as Sections of Higher-Dimensional Polytopes
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation
The electronic journal of combinatorics. - 22 (2015), 1, Artikel Nr. #P1.24
dcterms.bibliographicCitation.url
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p24
refubium.affiliation
Mathematik und Informatik
de
refubium.mycore.fudocsId
FUDOCS_document_000000024305
refubium.resourceType.isindependentpub
no
refubium.mycore.derivateId
FUDOCS_derivate_000000006219
dcterms.accessRights.openaire
open access
