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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| 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 |
| Sumario: | 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~$\frac{d}{400}$. |
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