Edges of the Barvinok-Novik orbitope

Details Edges of the Barvinok-Novik orbitope Edges of the Barvinok-Novik orbitope

2010-03-23

arxiv.org/abs/1003.4528v2

Discrete & Computational Geometry 46(33) (2011) pp. 479-487

Mathematics

Combinatorics

10 pages, 3 figures, corrected Lemma 4 and other minor revisions

Scientific paper

10.1007/s00454-011-9351-y

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.

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