M-convexity conjecture for Postnikov–Stanley polynomials

Postnikov–Stanley polynomials are a class of polynomials associated with permutations. A polynomial is M-convex when the set of exponent vectors of its monomials satisfies the discrete-exchange property defining an M-convex set. M-convexity conjecture. Every Postnikov–Stanley polynomial is M-convex. This would extend the paper's results on the M-convexity of Newton polytopes of dual Schubert polynomials to Postnikov–Stanley polynomials; the source presents it as a future direction and gives no resolution.