%0 Journal Article
%T Edges of the Barvinok-Novik orbitope
%A Cynthia Vinzant
%J Mathematics
%D 2010
%I arXiv
%R 10.1007/s00454-011-9351-y
%X 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.
%U http://arxiv.org/abs/1003.4528v2