Maps and $\Delta$-matroids revisited

TL;DR

This paper establishes a purely combinatorial definition of $$-matroids based on Tutte's maps and proves its equivalence to Bouchet's topological definition, bridging combinatorial and topological perspectives.

Contribution

It introduces a new combinatorial perspective on $$-matroids and proves their equivalence to existing topological definitions, unifying different approaches.

Findings

$$-matroids can be defined purely combinatorially using Tutte's maps

The combinatorial definition is shown to be equivalent to Bouchet's topological definition

Bridges the gap between combinatorial and topological approaches to $$-matroids

Abstract

Using Tutte's combinatorial definition of a map we define a $\Delta$-matroid purely combinatorially and show that it is identical to Bouchet's topological definition.