2017/05/14 by Stuart Margolis, Margolis, Stuart, John Rhodes +3
Computer Science · Mathematics · #05B35 #20E15 #20M99 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1705.04956
openalex publication_date 2017/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.