Symplectic Matroids, Circuits, and Signed Graphs

TL;DR

This paper introduces a circuit-based definition of symplectic matroids and constructs examples from graphs, advancing the theoretical understanding of these mathematical structures.

Contribution

It provides the first cryptomorphic circuit-based definition of symplectic matroids and demonstrates their construction from graphs.

Findings

Defined symplectic matroids via circuits

Constructed symplectic matroids from graphs

Extended the theoretical framework of symplectic matroids

Abstract

One generalization of ordinary matroids is symplectic matroids. While symplectic matroids were initially defined by their collections of bases, there has been no cryptomorphic definition of symplectic matroids in terms of circuits. We give a definition of symplectic matroids by collections of circuits. As an application, we construct a class of examples of symplectic matroids from graphs in terms of circuits.