On the matroids in which all hyperplanes are binary (Q1126303)

The main result of this paper is the following theorem: Let \(\mathcal M\) be a minor-closed class of matroids, and let \({\mathcal M}_1\) be the class of matroids for which the restriction to every hyperplane is in \(\mathcal M\). Then \({\mathcal M}_1\) is minor-closed and its set of excluded minors is \(\{ U_{1,1} \oplus N: N \hbox{ is an excluded minor for } {\mathcal M} \}\). This result is applied to matroids in which the restriction to every hyperplane is binary. Several alternative characterizations of this class of matroids are provided.