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- Title
The lattice of flats of a boolean representable simplicial complex.
- Authors
Margolis, Stuart; Rhodes, John; Silva, Pedro V.
- 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.
- Subjects
BOOLEAN algebra; LATTICE theory; LATTICE dynamics; GEOMETRIC vertices; NUMERICAL analysis
- Publication
International Journal of Algebra & Computation, 2018, Vol 28, Issue 8, p1677
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196718400131