Minkowski summands of cubes
Combinatorics
2022-04-26 v3
Abstract
In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit computations of type cones are in general intractable. Nevertheless, we show that the type cone of the product of simplices is the cone over a simplex. This remarkably simple result derives from insights about rainbow point configurations and the work of McMullen.
Keywords
Cite
@article{arxiv.2009.07252,
title = {Minkowski summands of cubes},
author = {Federico Castillo and Joseph Doolittle and Bennet Goeckner and Michael S. Ross and Li Ying},
journal= {arXiv preprint arXiv:2009.07252},
year = {2022}
}
Comments
12 pages, 4 figures. Incorporated referee suggestions, minor edits throughout. This version focuses more on type cones of products of simplices than the previous version. Introduction has been partially rewritten to reflect this change. To appear in the Bulletin of the London Mathematical Society