Newton polytopes of dual Schubert polynomials

TL;DR

This paper provides a complete combinatorial characterization of the supports and Newton polytopes of dual Schubert polynomials, offering an elementary proof of their M-convexity and detailing their vertices.

Contribution

It offers a new combinatorial description of the supports and vertices of dual Schubert polynomials' Newton polytopes, strengthening previous M-convexity results.

Findings

Supports of dual Schubert polynomials are fully characterized.

Vertices of their Newton polytopes are explicitly described.

Elementary proof of M-convexity is provided.

Abstract

The M-convexity of dual Schubert polynomials was first proven by Huh, Matherne, M\'esz\'aros, 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.