Lattice invariant valuations on rational polytopes
โ Scribed by P. McMullen
- Book ID
- 112500039
- Publisher
- Springer
- Year
- 1978
- Tongue
- English
- Weight
- 392 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0003-889X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A locally finite point set (such as the set Z n of integral points) gives rise to a lattice of polytopes in Euclidean space taking vertices from the given point set. We develop the combinatorial structure of this polytope lattice and derive Euler-type relations for valuations on polytopes using the
We give a classification of non-negative or Borel measurable, SLรฐdร invariant, homogeneous valuations on the space of d-dimensional convex polytopes containing the origin in their interiors. The only examples are volume, volume of the polar body, and the Euler characteristic.