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arXiv · 1510.05485

On the lattice of flats of a boolean representable simplicial complex

Stuart Margolis·John Rhodes·Pedro V. Silva
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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.

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Stuart Margolis, John Rhodes, Pedro V. Silva. 2015-10-19. On the lattice of flats of a boolean representable simplicial complex. https://arxiv.org/abs/1510.05485

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