Polytopes and large counterexamples

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.

References in corpus (1)

• Gelfand-Tsetlin polytopes and the integer decomposition property

Cited by in corpus (2)

• Restricted Birkhoff polytopes and Ehrhart period collapse
• Order Polytopes of Dimension $\le 13$ are Ehrhart Positive