Multimatroids IV. Chain-group representations Original Research Article

This paper completes the series A. Bouchet, Multimatroids I, SIAM J. Disc. Math.; A. Bouchet, Multimatroid II. Minors and connectivity; A. Bouchet, Multimatroids III. Tightness, fundamental graphs and pivotings, devoted to the introduction of multimatroids. Here we define a notion of linear representation that encompasses the isotropic systems and the linear representations of matroids and delta-matroids. We show that every Eulerian multimatroid is representable with a symplectic vector space over GF(2). Finally we adapt the construction to symplectic matroids.