2017/04/24 by Monika Ludwig, Laura Silverstein
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics #Equivariant map #Lattice (music) #Lift (data mining) #Mathematics #Point processes and geometric inequalities #Polytope #Pure mathematics #Rank (graph theory) #Tensor (intrinsic definition) #Tensor decomposition and applications #math.CO #math.MG #msc:52B20 #msc:52B45
paper · pdf · doi:10.1016/j.aim.2017.08.015
published as Adv. Math. 319 (2017), 76-110
arxiv created 2017/04/24 · openalex publication_date 2017/08/18 · arxiv updated 2021/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.