Using real algebraic geometry to solve combinatorial problems with symmetries

TL;DR

This paper explores how real algebraic geometry techniques can be applied to solve combinatorial problems with symmetries, highlighting methods, applications, and computational considerations.

Contribution

It provides a comprehensive overview of real algebraic geometry methods for combinatorial problems, including implementation and computational insights.

Findings

Real algebraic geometry effectively addresses symmetric combinatorial problems.

The paper reviews multiple applications of these methods.

Implementation details influence computational efficiency.

Abstract

Many combinatorial problems can be formulated as a polynomial optimization problem that can be solved by state-of-the-art methods in real algebraic geometry. In this paper we explain many important methods from real algebraic geometry, we review several applications and discuss implementation and computational aspects.