Polytopes and large counterexamples
Combinatorics
2018-09-26 v2
Abstract
In this short note, we give large counterexamples to natural questions about certain order polytopes, in particular, Gelfand--Tsetlin polytopes. Several of the counterexamples are too large to be discovered via a brute-force computer search. We also show that the multiset of hooks in a Young diagram is not enough information to determine the Ehrhart polynomial for an associated order polytope. This is somewhat counter-intuitive to the fact that the multiset of hooks always determine the leading coefficient of the Ehrhart polynomial.
Keywords
Cite
@article{arxiv.1609.00647,
title = {Polytopes and large counterexamples},
author = {Per Alexandersson},
journal= {arXiv preprint arXiv:1609.00647},
year = {2018}
}