On the subsemigroup complex of an aperiodic Brandt semigroup

Stuart Margolis, John Rhodes, Pedro V. Silva

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 languageEnglish
Pages (from-to)7-31
Number of pages25
JournalSemigroup Forum
Volume97
Issue number1
DOIs
StatePublished - 1 Aug 2018

Bibliographical note

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

Funding

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.

FundersFunder number
European structural funds
Simons Foundation
United States-Israel Binational Science Foundation2012080
Fundação para a Ciência e a Tecnologia
Centro de Matemática Universidade do PortoUID/MAT/00144/2013
European Regional Development FundPT2020

    Keywords

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

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