Fewnomial bounds for completely mixed polynomial systems

TL;DR

This paper establishes a new, tighter bound on the number of real solutions for a specific class of polynomial systems with distinct monomials across polynomials, improving upon existing fewnomial bounds by leveraging the structure of the system.

Contribution

It introduces a novel bound for the number of real solutions in completely mixed polynomial systems, considering the unique monomial structure to improve accuracy.

Findings

New bound for real solutions in completely mixed systems

Bound is tighter than general fewnomial bounds when structure is considered

Provides insights into the solution structure of such polynomial systems

Abstract

We give a bound for the number of real solutions to systems of n polynomials in n variables, where the monomials appearing in different polynomials are distinct. This bound is smaller than the fewnomial bound if this structure of the polynomials is not taken into account.