Monical's Saturated Newton Polytope Conjecture

If a chromatic symmetric function is Schur positive, must every finite-variable specialization $X_G(x_1, \dots, x_k)$ have a saturated Newton polytope? A $12$-vertex bipartite graph realizes weights $(6,6,0)$ and $(8,2,2)$ but omits their midpoint $(7,4,1)$.

Result

Disproved

Status

Resolved

AI contribution

AI-discovered

Method

Construction

Field

Newton polytopes

Posed by

Cara Monical, Neriman Tokcan & Alexander Yong

Year posed

2017

Years open

9y

Solved

2026-07-23

Model

ChatGPT-5.6 Sol Pro

Vendor

OpenAI

Collaborators

—

Verification

Unreviewed

Publication

Preprint

Significance

15 / 100*

Disclosed cost

—

Wikipedia

No dedicated article