A circuit axiomatisation of Lagrangian matroids Original Research Article

Characterisations of symplectic and orthogonal Lagrangian matroids in terms of basis exchange are well known. We define circuits of Lagrangian matroids in a natural way and characterise Lagrangian matroids in terms of circuit axioms. We go on to characterise orthogonal Lagrangian matroids in terms of circuits, and prove a result that may be useful in establishing orientations in terms of circuits.