Tensor valuations on lattice polytopes
Metric Geometry
2021-01-25 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1704.07177,
title = {Tensor valuations on lattice polytopes},
author = {Monika Ludwig and Laura Silverstein},
journal= {arXiv preprint arXiv:1704.07177},
year = {2021}
}