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math.MG2011★ 1 cited
Centrally symmetric polytopes with many faces
Alexander Barvinok, Seung Jin Lee, Isabella Novik
We present explicit constructions of centrally symmetric polytopes with many faces: first, we construct a d-dimensional centrally symmetric polytope P with about (1.316)^d vertices…
math.MG2011★ 5 cited
Neighborliness of the symmetric moment curve
Alexander Barvinok, Seung Jin Lee, Isabella Novik
We consider the convex hull B_k of the symmetric moment curve U(t)=(cos t, sin t, cos 3t, sin 3t, ..., cos (2k-1)t, sin (2k-1)t) in R^{2k}, where t ranges over the unit circle S= R…