Irreducibility of a sum of polynomials depending on disjoint sets of variables

TL;DR

This paper provides new sufficient conditions for the irreducibility of multivariable polynomials expressed as sums of polynomials with disjoint variable sets, using Newton polytope analysis and Gao's criterion.

Contribution

It introduces two novel irreducibility criteria for sums of polynomials with disjoint variables, expanding the theoretical understanding of polynomial irreducibility.

Findings

Two new sufficient conditions for irreducibility

Conditions based on Newton polytope analysis

Application of Gao's irreducibility criterion

Abstract

In this article, we give two different sufficient conditions for the irreducibility of a polynomial of more than one variable, over the field of complex numbers, that can be written as a sum of two polynomials which depend on mutually disjoint sets of variables. These conditions are derived from analyzing the Newton polytope of such a polynomial and then applying the `Irreducibility criterion' introduced by Gao.