Finite connectivity in infinite matroids

TL;DR

This paper introduces a connectivity function for infinite matroids that retains key properties of finite matroid connectivity, enabling the extension of Tutte's linking theorem to infinite cases.

Contribution

It defines a new connectivity function for infinite matroids and applies it to generalize Tutte's linking theorem to finitary and co-finitary matroids.

Findings

Connectivity function for infinite matroids with finite matroid properties

Extension of Tutte's linking theorem to infinite matroids

Preservation of submodularity and duality invariance

Abstract

We introduce a connectivity function for infinite matroids with properties similar to the connectivity function of a finite matroid, such as submodularity and invariance under duality. As an application we use it to extend Tutte's linking theorem to finitary and to co-finitary matroids.