Stanley's Claw-Free Schur-Positivity Conjecture

Is the chromatic symmetric function $X_G$ Schur positive for every claw-free graph $G$? Two explicit $12$-vertex line graphs have Schur coefficients $-64$ and $-40$ at $s_{(3,3,3,3)}$.

Result

Disproved

Status

Resolved

AI contribution

AI-discovered

Method

Construction

Field

Algebraic combinatorics

Posed by

Richard Stanley

Year posed

1995

Years open

31y

Solved

2026-07-23

Model

ChatGPT-5.6 Sol Pro

Vendor

OpenAI

Collaborators

—

Verification

Unreviewed

Publication

Preprint

Significance

25 / 100*

Disclosed cost

—

Wikipedia

No dedicated article