Edges of the Barvinok-Novik orbitope
Abstract
Here we study the kth 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 S1 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.
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