Algebraic matroids in action

TL;DR

This paper introduces algebraic matroids, a combinatorial framework for understanding algebraic independence, with applications in algebraic statistics and rigidity theory, emphasizing their unifying role in various applied mathematics fields.

Contribution

It provides a self-contained introduction to algebraic matroids and illustrates their potential applications through relevant examples.

Findings

Algebraic matroids formalize algebraic dependence and independence.

They unify concepts across algebraic statistics and rigidity theory.

The paper highlights the versatility of algebraic matroids in applied mathematics.

Abstract

In recent years, various notions of algebraic independence have emerged as a central and unifying theme in a number of areas of applied mathematics, including algebraic statistics and the rigidity theory of bar-and-joint frameworks. In each of these settings the fundamental problem is to determine the extent to which certain unknowns depend algebraically on given data. This has, in turn, led to a resurgence of interest in algebraic matroids, which are the combinatorial formalism for algebraic (in)dependence. We give a self-contained introduction to algebraic matroids together with examples highlighting their potential application.