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arXiv · 1609.00647

Polytopes and large counterexamples

Per Alexandersson
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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.

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Per Alexandersson. 2016-09-08. Polytopes and large counterexamples. https://doi.org/10.1080/10586458.2017.1361367

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