Many Neighborly Polytopes and Oriented Matroids

@article{Padrol2013ManyNP,
  title={Many Neighborly Polytopes and Oriented Matroids},
  author={Arnau Padrol},
  journal={Discrete & Computational Geometry},
  year={2013},
  volume={50},
  pages={865-902}
}
  • Arnau Padrol
  • Published 2013
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
In this paper we present a new technique to construct neighborly polytopes, and use it to prove a lower bound of $${\big (( r+d ) ^{( \frac{r}{2}+\frac{d}{2} )^{2}}\big )}\big /{\big ({r}^{{(\frac{r}{2})}^{2}} {d}^{{(\frac{d}{2})}^{2}}{\mathrm{e}^{3\frac{r}{2}\frac{d}{2}}}\big )}$$((r+d)(r2+d2)2)/(r(r2)2d(d2)2e3r2d2) for the number of combinatorial types of vertex-labeled neighborly polytopes in even dimension d with $$r+d+1$$r+d+1 vertices. This improves current bounds on the number of… Expand
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