On the subsemigroup complex of an aperiodic Brandt semigroup
Combinatorics
2017-05-16 v1
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.
Keywords
Cite
@article{arxiv.1705.04956,
title = {On the subsemigroup complex of an aperiodic Brandt semigroup},
author = {Stuart Margolis and John Rhodes and Pedro V. Silva},
journal= {arXiv preprint arXiv:1705.04956},
year = {2017}
}