Séminaire Lotharingien de Combinatoire, 93B.19 (2025), 12 pp.
Serena An, Katherine Tung and Yuchong Zhang
Newton Polytopes of Dual Schubert Polynomials
Abstract.
The M-convexity of the support of dual Schubert polynomials was first proven by Huh, Matherne, Mée;száros, and St. Dizier in 2022. We give a full characterization of the support 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.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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