Newton polytopes of dual Schubert polynomials

The M-convexity of dual Schubert polynomials was first proven by Huh, Matherne, Mészáros, and St. Dizier in 2022. We give a full characterization of the supports of dual Schubert polynomials, which yields an elementary alternative proof of the M-convexity result, and furthermore strengthens it by explicitly characterizing the vertices of their Newton polytopes combinatorially. Using this characterization, we give a polynomial-time algorithm to determine if a coefficient of a dual Schubert polynomial is zero, analogous to a result of Adve, Robichaux, and Yong for Schubert polynomials. This is a joint work with Yuchong Zhang, and there is a companion paper titled “Postnikov–Stanley Polynomials are Lorentzian.”

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