Extending a matroid by a cocircuit

Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view Dowling lattices and new results about line-closed geometries. We complement these topics by showing that line-closure gives simple geometric proofs of the (mostly known) basic results about Dowling lattices. We pursue the topic of line-closure further by showing how to construct some line-closed geometries that are not supersolvable.

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Joseph E. Bonin
• Keywords: DM 2006, Larger Matroid, Matroid, Simple Geometric Proofs