منابع مشابه
Minkowski valuations on lattice polytopes
A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over the integers and are translation invariant. In the contravariant case, the only such valuations are multiples of projection bodies. In the equivariant case, the only such valuations are generalized difference bodies combined with multiples of the newly defined disc...
متن کاملTensor valuations on lattice polytopes
The Ehrhart polynomial and the reciprocity theorems by Ehrhart & Macdonald are extended to tensor valuations on lattice polytopes. A complete classification is established of tensor valuations of rank up to eight that are equivariant with respect to the special linear group over the integers and translation covariant. Every such valuation is a linear combination of the Ehrhart tensors which is ...
متن کاملLocal tensor valuations on convex polytopes
Local versions of the Minkowski tensors of convex bodies in ndimensional Euclidean space are introduced. An extension of Hadwiger’s characterization theorem for the intrinsic volumes, due to Alesker, states that the continuous, isometry covariant valuations on the space of convex bodies with values in the vector space of symmetric p-tensors are linear combinations of modified Minkowski tensors....
متن کاملValuations and Tensor Weights on Polytopes
Let V be a finite-dimensional vector space over a square-root closed ordered field F (this restriction permits an inner product with corresponding norm to be imposed on V). Many properties of the family P :1⁄4 PðVÞ of convex polytopes in V can be expressed in terms of valuations (or finitely additive measures). Valuations such as volume, surface area and the Euler characteristic are translation...
متن کاملAn Euler Relation for Valuations on Polytopes
A locally finite point set (such as the set Z 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 language of Mo bius inversion. In this context a new family of inversion relations is obtained, the...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2009
ISSN: 0001-8708
DOI: 10.1016/j.aim.2008.09.004