Abstract
We introduce the subsemigroup complex of a finite semigroup S as a (boolean representable) simplicial complex defined through chains in the lattice of subsemigroups of S. We present a research program for such complexes, illustrated through the particular case of combinatorial Brandt semigroups. The results include alternative characterizations of faces and facets, asymptotical estimates on the number of facets, or establishing when the complex is pure or a matroid.
| Original language | English |
|---|---|
| Pages (from-to) | 7-31 |
| Number of pages | 25 |
| Journal | Semigroup Forum |
| Volume | 97 |
| Issue number | 1 |
| State | Published - 1 Aug 2018 |
Bibliographical note
Publisher Copyright:© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Boolean representable simplicial complex
- Brandt semigroup
- Lattice of subsemigroups
- Matroid
- Simplicial complex