Benchmarking libsemigroups

by Julius Jonušas and James Mitchell

In this post we present some performance benchmarks for the libsemigroups C++ library for semigroups and monoids. In particular, we present some experimental data about the performance of the add_generators method of the Semigroup class, and the parallel version of the Froidure-Pin algorithm described in our recent paper: J. Jonusas,... [Read More]

Congruence lattices of some famous semigroups

by James Mitchell

James East asked for some pictures of some congruences lattices of some famous semigroups, and I thought I’d post them here. The pictures in this post were created using the Semigroups package for GAP (the development version). The particular code for finding congruence lattices was written by Michael Torpey and... [Read More]

Counting monogenic semigroups

by James East and James Mitchell

In this post we show how to count the number of monogenic subsemigroups of the full transformation monoid up to isomorphism. Throughout this post, we denote the natural numbers \(\{0, 1, \ldots\}\) by \({\mathbb{N}}\). The symmetric group and full transformation semigroup on \(\{1, \ldots, n\}\), \(n\in {\mathbb{N}}\), are denoted \(S_n\)... [Read More]