Tensor valuations on lattice polytopes

Abstract

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 shown to no longer hold true for rank nine.

References in corpus (3)

• Combinatorial positivity of translation-invariant valuations and a discrete Hadwiger theorem
• Minkowski valuations on lattice polytopes
• Tensor valuations on lattice polytopes

Cited by in corpus (7)

• Tensor valuations on lattice polytopes
• Weighted Ehrhart Theory: Extending Stanley's nonnegativity theorem
• Geometric valuation theory
• Integral geometry of exceptional spheres
• Dimension of the space of unitary equivariant translation invariant tensor valuations
• Unimodular Valuations beyond Ehrhart
• $\mathrm{SL}(m,C)$-equivariant and translation covariant continuous tensor valuations