Split matroids and hypergraphs

Our paper titled Hypergraph characterization of split matroids is now available on arXiv. The paper studies the structure of split matroids from a combinatorial point of view. We introduce the notion of elementary split matroids and give a hypergraph characterization in terms of independent sets. The proposed class is closed not only under duality and taking minors but also truncation. Furthermore, in contrast to split matroids, it can be characterized by a single forbidden minor. As an application, we provide a complete list of binary split matroids.