Boolean Representations of Matroids and Lattices

Details Boolean Representations of Matroids and Lattices Boolean Representations of Matroids and Lattices

2011-08-06

arxiv.org/abs/1108.1473v3

Mathematics

Combinatorics

16 pages

Scientific paper

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.

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