naa a22 4500 510782604 CHVBK 20180411083252.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0107-z doi (NATIONALLICENCE)springer-10.1007/s11856-012-0107-z Centrally symmetric polytopes with many faces [Elektronische Daten] [Alexander Barvinok, Seung Lee, Isabella Novik] We present explicit constructions of centrally symmetric polytopes with many faces: (1) we construct a d-dimensional centrally symmetric polytope P with about 3 d/4 ≈ (1.316) d vertices such that every pair of non-antipodal vertices of P spans an edge of P, (2) for an integer k ≥ 2, we construct a d-dimensional centrally symmetric polytope P of an arbitrarily high dimension d and with an arbitrarily large number N of vertices such that for some 0 < δ k < 1 at least (1 − (δ k ) d )( k N ) k-subsets of the set of vertices span faces of P, and (3) for an integer k ≥ 2 and α > 0, we construct a centrally symmetric polytope Q with an arbitrarily large number of vertices N and of dimension d = k 1+o(1) such that at least $(1 - k^{ - \alpha } )(_k^N )$ k-subsets of the set of vertices span faces of Q. Hebrew University Magnes Press, 2013 Barvinok Alexander Department of Mathematics, University of Michigan, 48109-1043, Ann Arbor, MI, USA aut Lee Seung Department of Mathematics, University of Michigan, 48109-1043, Ann Arbor, MI, USA aut Novik Isabella Department of Mathematics, University of Washington, 98195-4350, Seattle, WA, USA aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/1(2013-06-01), 457-472 0021-2172 195:1<457 2013 195 11856 https://doi.org/10.1007/s11856-012-0107-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0107-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Barvinok Alexander Department of Mathematics, University of Michigan, 48109-1043, Ann Arbor, MI, USA aut NATIONALLICENCE 700 1- Lee Seung Department of Mathematics, University of Michigan, 48109-1043, Ann Arbor, MI, USA aut NATIONALLICENCE 700 1- Novik Isabella Department of Mathematics, University of Washington, 98195-4350, Seattle, WA, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/1(2013-06-01), 457-472 0021-2172 195:1<457 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer