A new presentation for the inner Tutte group of a matroid

TL;DR

This paper introduces a novel, more concise presentation of the inner Tutte group of a matroid, enhancing understanding of its algebraic structure and simplifying its analysis.

Contribution

It provides a new, smaller generating set for the inner Tutte group, improving upon previous presentations and facilitating further research.

Findings

A new presentation reduces the number of generators needed.

Simplifies the algebraic understanding of the inner Tutte group.

Potentially aids in computational and theoretical applications.

Abstract

The inner Tutte group of a matroid is a finitely generated abelian group introduced as an algebraic counterpart of Tutte's homotopy theory of matroids. The aim of this work is to provide a new presentation for this group with a set of generators that is smaller than those previously known.