On the subsemigroup complex of an aperiodic Brandt semigroup

Stuart Margolis, John Rhodes, Pedro V. Silva

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish
Pages (from-to)7-31
Number of pages25
JournalSemigroup Forum
Issue number1
StatePublished - 1 Aug 2018

Bibliographical note

Funding Information:
Acknowledgements Stuart Margolis acknowledges support from the Binational Science Foundation (BSF) of the United States and Israel, Grant Number 2012080. John Rhodes acknowledges support from the Simons Foundation. Pedro V. Silva was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER), under the partnership agreement PT2020.

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.


  • Boolean representable simplicial complex
  • Brandt semigroup
  • Lattice of subsemigroups
  • Matroid
  • Simplicial complex


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