77 citations · 153 across the 17 of their papers we have counts for
26 papers
On the minimal faithful degree of Rhodes semisimple semigroups
Stuart Margolis, Benjamin Steinberg
In this paper we compute the minimum degree of a faithful representation by partial transformations of a finite semigroup admitting a faithful completely reducible matrix represent…
Decidability of Krohn-Rhodes complexity of finite semigroups and automata
Stuart Margolis, John Rhodes, Anne Schilling
When decomposing a finite semigroup into a wreath product of groups and aperiodic semigroups, complexity measures the minimal number of groups that are needed. Determining an algor…
Ehresmann Semigroups Whose Categories are EI and Their Representation Theory : Extended Version
Stuart Margolis, Itamar Stein
We study simple and projective modules of a certain class of Ehresmann semigroups, a well-studied generalization of inverse semigroups. Let be a finite right (left) restriction…
Degree 2 Transformation Semigroups as Continuous Maps on Graphs: Foundations and Structure
Stuart W. Margolis, John Rhodes
We develop the theory of transformation semigroups that have degree 2, that is, act by partial functions on a finite set such that the inverse image of points have at most two elem…
Truncated Boolean Representable Simplicial Complexes
Stuart W. Margolis, John Rhodes, Pedro Silva
We extend, in significant ways, the theory of truncated boolean representable simplicial complexes introduced in 2015. This theory, which includes all matroids, represents the larg…
On the Wilson Monoid of a Pairwise Balanced Design
Stuart W. Margolis, John Rhodes, Pedro Silva
We give a new perspective of the relationship between simple matroids of rank 3 and pairwise balanced designs, connecting Wilson's theorems and tools with the theory of truncated b…