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- Title
On the subsemigroup complex of an aperiodic Brandt semigroup.
- Authors
Margolis, Stuart; Rhodes, John; Silva, Pedro V.
- 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.
- Subjects
LATTICE theory; GROUP theory; SET theory; MATHEMATICAL transformations; QUANTUM mechanics
- Publication
Semigroup Forum, 2018, Vol 97, Issue 1, p7
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-018-9927-4