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...
| Author: | |
|---|---|
| Format: | article |
| Publication Date: | 2006 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/434 |
| Online Access: | https://hdl.handle.net/2117/434 |
| Access Level: | Open access |
| Keyword: | 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 |
| Summary: | 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~$\frac{d}{400}$. |
|---|