Newton polytope of good symmetric polynomials

TL;DR

This paper introduces a broad class of symmetric polynomials with saturated Newton polytopes and integer decomposition properties, unifying many previously studied cases in a single framework.

Contribution

It defines a new class of symmetric polynomials with specific geometric properties, extending the understanding of their Newton polytopes.

Findings

The class covers many previously studied symmetric polynomials.

The Newton polytopes of these polynomials are saturated and have integer decomposition.

Provides a unified geometric framework for symmetric polynomials.

Abstract

We introduce a general class of symmetric polynomials that have saturated Newton polytope and their Newton polytope has integer decomposition property. The class covers numerous previously studied symmetric polynomials.