Ehrhart positivity of Schubitopes
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A Schubitope is a lattice polytope associated with diagram data. Its Ehrhart polynomial counts lattice points in positive integer dilations. Must every coefficient of that polynomial be nonnegative?
Why it matters and what counts as progress
Why it matters: The conjecture proposes a coefficient-positivity property beyond the positivity of the lattice-point counts themselves.
What counts as progress: A positivity theorem or a fully specified Schubitope with an exactly computed negative Ehrhart coefficient.
How the problem developed
- 7 Mar 2017 · Conjecture [1]
Cara Monical, Neriman Tokcan and Alexander Yong Introduced Schubitopes and conjectured that every Schubitope has an Ehrhart polynomial with nonnegative coefficients.
- 1 Aug 2026 · Counterexample [2]
Yupeng Li and Avery St. Dizier, using GPT-5.6 Sol Pro in ChatGPT Exhibited a Schubitope with a negative Ehrhart coefficient, disproving the conjecture. The authors credit GPT-5.6 Sol Pro with finding the example.
AI contribution
Schubitopes are not Ehrhart positive
The Schubitope in R¹⁴ from columns {8,…,14} and {12,13,14}, equivalently Δ(7,14)+Δ(3,14), has Ehrhart quadratic coefficient −687323/79200. It is therefore not Ehrhart positive.
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