A centrally symmetric version of the cyclic polytope

2006/11/28 by Alexander Barvinok, Isabella Novik, Barvinok, Alexander +1
Mathematics · #52A20 #52B12 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.math/0611893

openalex publication_date 2006/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 c₁(d) ≥ (d-2)/(d-1).

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