Local neighborliness of the symmetric moment curve

Details Local neighborliness of the symmetric moment curve Local neighborliness of the symmetric moment curve

2011-02-25

arxiv.org/abs/1102.5143v1

Mathematics

Combinatorics

Scientific paper

A centrally symmetric analogue of the cyclic polytope, the bicyclic polytope, was defined in [BN08]. The bicyclic polytope is defined by the convex hull of finitely many points on the symmetric moment curve where the set of points has a symmetry about the origin. In this paper, we study the Barvinok-Novik orbitope, the convex hull of the symmetric moment curve. It was proven in [BN08] that the orbitope is locally $k$-neighborly, that is, the convex hull of any set of $k$ distinct points on an arc of length not exceeding $\phi_k$ in $\mathbb{S}^1$ is a $(k-1)$-dimensional face of the orbitope for some positive constant $\phi_k$. We prove that we can choose $\phi_k $ bigger than $\gamma k^{-3/2} $ for some positive constant $\gamma$.

Affiliated with

Also associated with

No associations

Rating

Local neighborliness of the symmetric moment curve does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Local neighborliness of the symmetric moment curve, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local neighborliness of the symmetric moment curve will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-709193