Boolean Representations of Matroids and Lattices
Combinatorics
2012-02-01 v3 Commutative Algebra
Rings and Algebras
Representation Theory
Abstract
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.
Cite
@article{arxiv.1108.1473,
title = {Boolean Representations of Matroids and Lattices},
author = {Zur Izhakian and John Rhodes},
journal= {arXiv preprint arXiv:1108.1473},
year = {2012}
}
Comments
16 pages