Matroids, hereditary collections and simplicial complexes having boolean representations

Abstract

Inspired by the work of Izakhian and Rhodes, a theory of representation of hereditary collections by boolean matrices is developed. This corresponds to representation by finite $\vee$-generated lattices. The lattice of flats, defined for hereditary collections, lattices and matrices, plays a central role in the theory. The representations constitute a lattice and the minimal and strictly join irreducible elements are studied, as well as various closure operators.

57 pages

References in corpus (3)

• Boolean Representations of Matroids and Lattices
• The Tropical Rank of a Tropical Matrix
• C-independence and c-rank of posets and lattices