An explicit construction for neighborly centrally symmetric polytopes

We give an explicit construction, based on Hadamard matrices, for an infinite series of $\big\lfloor\frac12\sqrt{d}\big\rfloor$-neighborly centrally symmetric $d$-dimensional polytopes with $4d$~vertices. This appears to be the best explicit version yet of a recent probabilistic result due to Linial...

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Detalles Bibliográficos
Autor: Pfeifle, Julián|||0000-0001-9777-2602
Tipo de recurso: artículo
Fecha de publicación:2006
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/434
Acceso en línea:https://hdl.handle.net/2117/434
Access Level:acceso abierto
Palabra clave:Discrete geometry
Polytopes
cs-transform
Hadamard matrix
generalized inverse
Geometria combinatòria
Geometria discreta
Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
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spelling An explicit construction for neighborly centrally symmetric polytopesPfeifle, Julián|||0000-0001-9777-2602Discrete geometryPolytopescs-transformHadamard matrixgeneralized inverseGeometria combinatòriaGeometria discretaClassificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedraÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discretaWe give an explicit construction, based on Hadamard matrices, for an infinite series of $\big\lfloor\frac12\sqrt{d}\big\rfloor$-neighborly centrally symmetric $d$-dimensional polytopes with $4d$~vertices. This appears to be the best explicit version yet of a recent probabilistic result due to Linial and Novik, who proved the existence of such polytopes with a neighborliness of~$\frac{d}{400}$.20062006-06-2920062006-07-12journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/434reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-ShareAlike 2.5 Spainhttp://creativecommons.org/licenses/by-nc-sa/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4342026-05-27T15:37:01Z
dc.title.none.fl_str_mv An explicit construction for neighborly centrally symmetric polytopes
title An explicit construction for neighborly centrally symmetric polytopes
spellingShingle An explicit construction for neighborly centrally symmetric polytopes
Pfeifle, Julián|||0000-0001-9777-2602
Discrete geometry
Polytopes
cs-transform
Hadamard matrix
generalized inverse
Geometria combinatòria
Geometria discreta
Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
title_short An explicit construction for neighborly centrally symmetric polytopes
title_full An explicit construction for neighborly centrally symmetric polytopes
title_fullStr An explicit construction for neighborly centrally symmetric polytopes
title_full_unstemmed An explicit construction for neighborly centrally symmetric polytopes
title_sort An explicit construction for neighborly centrally symmetric polytopes
dc.creator.none.fl_str_mv Pfeifle, Julián|||0000-0001-9777-2602
author Pfeifle, Julián|||0000-0001-9777-2602
author_facet Pfeifle, Julián|||0000-0001-9777-2602
author_role author
dc.subject.none.fl_str_mv Discrete geometry
Polytopes
cs-transform
Hadamard matrix
generalized inverse
Geometria combinatòria
Geometria discreta
Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
topic Discrete geometry
Polytopes
cs-transform
Hadamard matrix
generalized inverse
Geometria combinatòria
Geometria discreta
Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
description We give an explicit construction, based on Hadamard matrices, for an infinite series of $\big\lfloor\frac12\sqrt{d}\big\rfloor$-neighborly centrally symmetric $d$-dimensional polytopes with $4d$~vertices. This appears to be the best explicit version yet of a recent probabilistic result due to Linial and Novik, who proved the existence of such polytopes with a neighborliness of~$\frac{d}{400}$.
publishDate 2006
dc.date.none.fl_str_mv 2006
2006-06-29
2006
2006-07-12
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/434
url https://hdl.handle.net/2117/434
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-ShareAlike 2.5 Spain
http://creativecommons.org/licenses/by-nc-sa/2.5/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-ShareAlike 2.5 Spain
http://creativecommons.org/licenses/by-nc-sa/2.5/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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