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Monical's Saturated Newton Polytope Conjecture

Combinatorics · posed by Cara Monical, Neriman Tokcan & Alexander Yong, 2017 · disproved

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Statement

If a chromatic symmetric function is Schur positive, must every finite-variable specialization XG(x1,…,xk)X_G(x_1, \dots, x_k) have a saturated Newton polytope? A 1212-vertex bipartite graph realizes weights (6,6,0)(6,6,0) and (8,2,2)(8,2,2) but omits their midpoint (7,4,1)(7,4,1).

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    ChatGPT-5.6 Sol Pro

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    The finite witness was found with ChatGPT-5.6 Sol Pro and verified by direct computation.

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