Utilize este identificador para referenciar este registo:
https://hdl.handle.net/10316/44073
Campo DC | Valor | Idioma |
---|---|---|
dc.contributor.author | Gouveia, João | - |
dc.contributor.author | Pashkovich, Kanstanstin | - |
dc.contributor.author | Robinson, Richard Z. | - |
dc.contributor.author | Thomas, Rekha R. | - |
dc.date.accessioned | 2017-10-20T17:09:46Z | - |
dc.date.issued | 2017 | - |
dc.identifier.uri | https://hdl.handle.net/10316/44073 | - |
dc.description.abstract | The positive semidefinite (psd) rank of a polytope is the size of the smallest psd cone that admits an affine slice that projects linearly onto the polytope. The psd rank of a d-polytope is at least d+1, and when equality holds we say that the polytope is psd-minimal. In this paper we develop new tools for the study of psd-minimality and use them to give a complete classification of psd-minimal 4-polytopes. The main tools introduced are trinomial obstructions, a new algebraic obstruction for psd-minimality, and the slack ideal of a polytope, which encodes the space of realizations of a polytope up to projective equivalence. Our central result is that there are 31 combinatorial classes of psd-minimal 4-polytopes. We provide combinatorial information and an explicit psd-minimal realization in each class. For 11 of these classes, every polytope in them is psd-minimal, and these are precisely the combinatorial classes of the known projectively unique 4-polytopes. We give a complete characterization of psd-minimality in the remaining classes, encountering in the process counterexamples to some open conjectures. | por |
dc.language.iso | eng | por |
dc.publisher | Elsevier | por |
dc.relation | info:eu-repo/grantAgreement/FCT/5876/147205/PT | por |
dc.rights | embargoedAccess | - |
dc.title | Four-dimensional polytopes of minimum positive semidefinite rank | por |
dc.type | article | - |
degois.publication.firstPage | 184 | por |
degois.publication.lastPage | 226 | por |
degois.publication.title | Journal of Combinatorial Theory, Series A | por |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0097316516300747 | por |
dc.peerreviewed | yes | por |
dc.identifier.doi | 10.1016/j.jcta.2016.08.002 | por |
dc.identifier.doi | 10.1016/j.jcta.2016.08.002 | - |
degois.publication.volume | 145 | por |
dc.date.embargo | 2019-10-20T17:09:46Z | - |
uc.controloAutoridade | Sim | - |
item.grantfulltext | open | - |
item.cerifentitytype | Publications | - |
item.languageiso639-1 | en | - |
item.openairetype | article | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.fulltext | Com Texto completo | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0001-8345-9754 | - |
Aparece nas coleções: | I&D CMUC - Artigos em Revistas Internacionais |
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