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.
| Original language | English |
|---|---|
| Pages (from-to) | 1677-1691 |
| Number of pages | 15 |
| Journal | International Journal of Algebra and Computation |
| Volume | 28 |
| Issue number | 8 |
| DOIs | |
| State | Published - 1 Dec 2018 |
Bibliographical note
Publisher Copyright:© 2018 World Scientific Publishing Company.
Funding
The third author was partially supported by CNPq (Brazil) through a BJT-A grant (process 313768/2013-7) and CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020. The second author thanks the Simons Foundation-Collaboration Grants for Mathematicians for travel grant #313548. The first author was partially supported by Binational Science Foundation grant number 2012080.
| Funders | Funder number |
|---|---|
| European structural funds | |
| Simons Foundation-Collaboration Grants for Mathematicians | 313548 |
| United States-Israel Binational Science Foundation | 2012080 |
| Fundação para a Ciência e a Tecnologia | |
| Conselho Nacional de Desenvolvimento Científico e Tecnológico | 313768/2013-7 |
| Centro de Matemática Universidade do Porto | UID/MAT/00144/2013 |
| European Regional Development Fund | PT2020 |
Keywords
- Simplicial complex
- atomistic lattice
- boolean representable
- hereditary collection
- lattice of flats