Browse issues
no. 6
Newton polytopes of dual Schubert polynomials
An, Serena1; Tung, Katherine2; Zhang, Yuchong3
1 Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA 02139 (USA)
2 Harvard University, Department of Mathematics, Cambridge, MA 02138 (USA)
3 University of Michigan, Department of Mathematics, Ann Arbor, MI 48109 (USA)
Algebraic Combinatorics, Volume 8 (2025) no. 6, pp. 1459-1472

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 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:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.450
Classification: 05E05, 14N15, 52B40
Keywords: Newton polytope, dual Schubert polynomial, M-convex

An, Serena 1; Tung, Katherine 2; Zhang, Yuchong 3

1 Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA 02139 (USA)
2 Harvard University, Department of Mathematics, Cambridge, MA 02138 (USA)
3 University of Michigan, Department of Mathematics, Ann Arbor, MI 48109 (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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An, Serena; Tung, Katherine; Zhang, Yuchong. Newton polytopes of dual Schubert polynomials. Algebraic Combinatorics, Volume 8 (2025) no. 6, pp. 1459-1472. doi: 10.5802/alco.450

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