Edges of the Barvinok-Novik orbitope
Combinatorics
2015-03-13 v2 Metric Geometry
Abstract
Here we study the k^th symmetric trigonometric moment curve and its convex hull, the Barvinok-Novik orbitope. In 2008, Barvinok and Novik introduce these objects and show that there is some threshold so that for two points on S^1 with arclength below this threshold, the line segment between their lifts on the curve form an edge on the Barvinok-Novik orbitope and for points with arclenth above this threshold, their lifts do not form an edge. They also give a lower bound for this threshold and conjecture that this bound is tight. Results of Smilansky prove tightness for k=2. Here we prove this conjecture for all k.
Cite
@article{arxiv.1003.4528,
title = {Edges of the Barvinok-Novik orbitope},
author = {Cynthia Vinzant},
journal= {arXiv preprint arXiv:1003.4528},
year = {2015}
}
Comments
10 pages, 3 figures, corrected Lemma 4 and other minor revisions