Convex Polytopes: Extremal Constructions and f -Vector Shapes

@article{Ziegler2007ConvexPE,
  title={Convex Polytopes: Extremal Constructions and f -Vector Shapes},
  author={G. Ziegler},
  journal={arXiv: Metric Geometry},
  year={2007}
}
  • G. Ziegler
  • Published 2007
  • Mathematics
  • arXiv: Metric Geometry
The study of f -vectors has had huge successes in the last forty years. The most fundamental one is undoubtedly the “g-theorem,” conjectured by McMullen in 1971 and proved by Billera & Lee and Stanley in 1980, which characterizes the f vectors of simplicial and of simple polytopes combinatorially. See also Section 5.2 of Forman’s article in this volume, where h-vectors are discu ssed in connection with the Charney–Davis conjecture. Nevertheless, on some fundamental problems embarassingly little… Expand
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