On the subsemigroup complex of an aperiodic Brandt semigroup

Stuart Margolis; John Rhodes; Pedro V. Silva

doi:10.1007/s00233-018-9927-4

On the subsemigroup complex of an aperiodic Brandt semigroup

Stuart Margolis, John Rhodes, Pedro V. Silva

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 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 language	English
Pages (from-to)	7-31
Number of pages	25
Journal	Semigroup Forum
Volume	97
Issue number	1
DOIs	https://doi.org/10.1007/s00233-018-9927-4
State	Published - 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.

Keywords

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

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10.1007/s00233-018-9927-4

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On the subsemigroup complex of an aperiodic Brandt semigroup

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