Supersymmetric Schur polynomials have saturated Newton polytopes

TL;DR

This paper proves that all supersymmetric Schur polynomials possess a saturated Newton polytope, using a tableau-based approach and polyhedral combinatorics to establish integrality and the SNP property.

Contribution

It introduces a novel tableau-theoretic and polyhedral method to prove the saturated Newton polytope property for supersymmetric Schur polynomials.

Findings

All supersymmetric Schur polynomials have saturated Newton polytopes.

The support of these polynomials can be described by a totally unimodular polyhedron.

The proof uses Hoffman-Kruskal criterion for integrality.

Abstract

We prove that every supersymmetric Schur polynomial has a saturated Newton polytope (SNP). Our approach begins with a tableau-theoretic description of the support, which we encode as a polyhedron with a totally unimodular constraint matrix. The integrality of this polyhedron follows from the Hoffman-Kruskal criterion, thereby establishing the SNP property.