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# Tag Archives: permutation groups

## Fair games and Artin’s conjecture

A few years ago I described Persi Diaconis’ response to G. H. Hardy’s claim that there is a real dividing line between real and recreational mathematics. (See the report here.) This led from Persi’s first experiments in card shuffling to Artin’s conjecture … Continue reading

## Books

I realised yesterday that, although I had moved the web pages of books I had written to my St Andrews website when I came here, I had neither updated them nor put links to them. I have done the easier … Continue reading

Posted in books, the Web
Tagged algebra, combinatorics, logic, permutation groups, set theory
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## Dugald Macpherson’s birthday meeting

Still catching up on the backlog: last week I was in Edinburgh for a meeting at ICMS for Dugald Macpherson’s birthday. The ICMS has just moved to new premises at the top of the University of Edinburgh’s new Bayes Centre, … Continue reading

## 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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## From permutation groups to model theory

I cannot resist a conference with a title like this! But in this case, there is another very important reason to attend. In the mid-1970s, when I began being interested in infinite permutation groups (I had been a strictly finite … Continue reading

Posted in events, history
Tagged Dugald Macpherson, ICMS, model theory, permutation groups
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## Symmetry vs Regularity

This is the title of a conference to be held next year (2018) from 1 to 7 July, in Pilsen, Bohemia, Czech Republic. The subtitle is “The first 50 years since Weisfeiler-Leman stabilization”, and the webpage is here. If you … Continue reading

## Summer school at Marienheide

Last week, I was lecturing at a summer school in Franz Dohrmann Haus, a very pleasant conference centre in the small town of Marienheide, not far from Köln. Apart from a walk on Wednesday afternoon, I didn’t get much exercise, … Continue reading

Posted in events
Tagged Cheryl Praeger, Csaba Schneider, O'Nan-Scott theorem, Pablo Spiga, permutation groups
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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

## 12160

12160 is an interesting number; but I didn’t know that until last night. As part of the work on semigroups, we are looking at the following problem. Given n and k, with n ≥ 2k, suppose that G is a k-homogeneous subgroup … Continue reading

Posted in doing mathematics, exposition
Tagged 4-homogeneous, permutation groups, semigroups
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## Permutation groups and transformation semigroups

When I first decided to apply to the LMS to run a Durham symposium on Permutation Groups and Transformation Semigroups, I had a fairly clear idea of what I wanted: topics (both finite and infinite) where the techniques and results … Continue reading