Schubitopes are not Ehrhart positive

Abstract

Schubitopes are a family of generalized permutahedra arising as the Newton polytopes of both Schubert polynomials and Demazure characters of ${\mathrm{GL}}_n$. Monical, Tokcan, and Yong conjectured that Schubitopes are Ehrhart positive. We exhibit a counterexample to this conjecture, a Schubitope whose Ehrhart polynomial contains a negative coefficient in its monomial expansion. This example was found using GPT-5.6 Sol Pro in ChatGPT.

8 pages, 3 figures