On Kalai's conjectures concerning centrally symmetric polytopes
Combinatorics
2012-12-27 v2 Metric Geometry
Abstract
In 1989 Kalai stated the three conjectures A, B, C of increasing strength concerning face numbers of centrally symmetric convex polytopes. The weakest conjecture, A, became known as the ``-conjecture''. It is well-known that the three conjectures hold in dimensions d \leq 3. We show that in dimension 4 only conjectures A and B are valid, while conjecture C fails. Furthermore, we show that both conjectures B and C fail in all dimensions d \geq 5.
Keywords
Cite
@article{arxiv.0708.3661,
title = {On Kalai's conjectures concerning centrally symmetric polytopes},
author = {Raman Sanyal and Axel Werner and Günter M. Ziegler},
journal= {arXiv preprint arXiv:0708.3661},
year = {2012}
}
Comments
14 pages; minor corrections and notational adjustments