A q-analogue of delta-matroids and related concepts

TL;DR

This paper introduces q-delta-matroids and q-g-matroids, extending classical matroid concepts to finite-dimensional vector spaces over finite fields, and compares their axiomatic and structural definitions.

Contribution

It defines and studies q-analogues of delta-matroids and g-matroids, providing new frameworks for matroid theory over finite fields.

Findings

Introduction of q-delta-matroids and q-g-matroids

Comparison of axiomatic and strong map definitions

Extension of matroid concepts to vector spaces over finite fields

Abstract

We define and study q-delta-matroids, and q-g-matroids. These objects are analogues, for finite-dimensional vector spaces over finite fields, of delta-matroids and g-matroids arising from finite sets. We compare axiomatic descriptions with definitions by means of strong maps of q-matroids.