A centrally symmetric version of the cyclic polytope

Details A centrally symmetric version of the cyclic polytope A centrally symmetric version of the cyclic polytope

2006-11-28

arxiv.org/abs/math/0611893v1

Mathematics

Combinatorics

23 pages, 2 figures

Scientific paper

We define a centrally symmetric analogue of the cyclic polytope and study its facial structure. We conjecture that our polytopes provide asymptotically the largest number of faces in all dimensions among all centrally symmetric polytopes with n vertices of a given even dimension d=2k when d is fixed and n grows. For a fixed even dimension d=2k and an integer 0< j 0 and at most (1-2^{-d}+o(1)){n \choose j+1} as n grows. We show that c_1(d) \geq (d-2)/(d-1).

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