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Tag Archives: regular semigroups
The existential transversal property
One of the first things that João Araújo introduced me to when we started collaborating, after synchronization, was the universal transversal property: a permutation group G on the set {1,…,n} has the k-universal transversal property (k-ut for short) if, given … Continue reading
Posted in exposition
Tagged partitions, permutation groups, regular semigroups, transversals
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A week in Vienna
Last week, in the second week of Spring break in St Andrews, I was in Vienna, giving a course of lectures to the PhD students, at the invitation of Tomack Gilmore, a Queen Mary undergraduate now finishing his PhD with … Continue reading
A visit to Lisbon
Back in London after three weeks in Lisboa. It wasn’t meant to be my research visit; I tagged along with the intention of having a holiday. But it didn’t work out like that. We lived in student accommodation at the … Continue reading
Posted in doing mathematics, exposition, synchronization
Tagged fado, regular semigroups, royal palaces, synchronization
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Permutation groups and regular semigroups, 2
João Araújo and I have been working together this week, and the paper, which I discussed here, is nearly ready to submit, after we managed a couple of quite significant improvements. I’d like to draw attention to a couple of … Continue reading
Posted in mathematics, open problems
Tagged homogeneous, Livingstone, regular semigroups, set-transitive, universal transversal property, Wagner
7 Comments
Permutation groups and regular semigroups
This week, I gave a talk in the Pure Mathematics seminar explaining what João Araújo and I have been up to this summer. I will try to summarise here. João believes that semigroup theorists have shied away from studying the … Continue reading