This is an expository paper on connections between enumerative combinatorics and convex polytopes. It aims to give an essentially self-contained overview of five specific instances when enumerative combinatorics and convex polytopes arise jointly in problems whose initial formulation lies in only on
Heights of convex polytopes
β Scribed by Victor Klee
- Publisher
- Elsevier Science
- Year
- 1965
- Tongue
- English
- Weight
- 663 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
to branko gru nbaum in honor of his seventieth birthday An inner diagonal of a polytope P is a segment that joins two vertices of P and that lies, except for its ends, in P's relative interior. The paper's main results are as follows: (a) Among all d-polytopes P having a given number v of vertices,
It is shown that if three vertices of the graph c?(l)) of a convex 3-polytope P are chosen, then G(P) contains a refinement of the complete graph C,, on four vertices, for which the three chosen vertices are principal (that is, correspond to vertices of C, in the refinement.. In general, all four ve