On the lattice of flats of a boolean representable simplicial complex
Combinatorics
2015-10-20 v1
Abstract
It is shown that the lattices of flats of boolean representable simplicial complexes are always atomistic, but semimodular if and only if the complex is a matroid. A canonical construction is introduced for arbitrary finite atomistic lattices, providing a characterization of the lattices of flats of boolean representable simplicial complexes and a decidability condition. We remark that every finite lattice occurs as the lattice of flats of some simplicial complex.
Keywords
Cite
@article{arxiv.1510.05485,
title = {On the lattice of flats of a boolean representable simplicial complex},
author = {Stuart Margolis and John Rhodes and Pedro V. Silva},
journal= {arXiv preprint arXiv:1510.05485},
year = {2015}
}
Comments
15 pages