Combinatorial Methods for Minkowski Tensors of Polytopes
Combinatorics
2020-07-28 v1 Metric Geometry
Abstract
In this paper we use a generating function approach to record and calculate entries of the Minkowski tensors of a polytope. We focus on ''surface tensors'', extending the methods used in arXiv:1807.10258 for moments of the uniform distribution which correspond to volume tensors. In this context we also extend the definition of the adjoint polynomial to the boundary complex of a polytope with simplicial facets. In the case of simplicial polytopes we give an explicit formulation for these surface tensors.
Keywords
Cite
@article{arxiv.2007.12893,
title = {Combinatorial Methods for Minkowski Tensors of Polytopes},
author = {Niklas Livchitz and Büşra Sert and Amy Wiebe},
journal= {arXiv preprint arXiv:2007.12893},
year = {2020}
}