The lattice of flats of a boolean representable simplicial complex

• Type: Article in International Scientific Journal
• Date: 2018

Authors

Margolis, S (Author) Other; Rhodes, J (Author) Other; Pedro V. Silva (Author) FCUP

Journal

Title: International Journal of Algebra and Computation

Vol. 28

Pages: 1677-1691

ISSN: 0218-1967

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00P-P6V

DOI: 10.1142/s0218196718400131

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15