Boolean Representations of Matroids and Lattices
  We introduce a new representation concept for lattices by boolean matrices, and utilize it to prove that any matroid is boolean representable. We show that such a representation can be easily extracted from a representation of the associated lattice of flats of the matroid, leading also to a tighter bound on the representation's size. Consequently, we obtain a linkage of boolean representations with geometry in a very natural way. 
Zur Izhakian, John Rhodes
math.CO math.AC math.RA math.RT