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# Tag Archives: permutation groups

## 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
3 Comments

## 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

## Real v recreational mathematics

A footnote to my report on Persi Diaconis’ lecture on Martin Gardner. Persi challenged us to consider the question: Is there a sharp division between “real” mathematics and “recreational” mathematics, and if so, where does it come? G. H. Hardy clearly thought … Continue reading

Posted in exposition
Tagged Bill Kantor, G. H. Hardy, perfect shuffles, permutation groups, Persi Diaconis, Ron Graham
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## A thrifty algorithm

Two important classical parameters of a permutation group G of degree n are the base size, the smallest size of a collection of points whose pointwise stabiliser is the identity; and the minimal degree, the smallest number of points moved … Continue reading

Posted in exposition, open problems
Tagged base size, greedy algorithm, Kenneth Blaha, minimal degree, permutation groups, primitive groups
4 Comments

## A permutation group challenge, 2

The result in the preceding post can be formulated as follows: A permutation group of degree n = 2k which is transitive on partitions of shape (k,k) but not on ordered partitions of this shape, has a fixed point and is (k−1)-homogeneous … Continue reading

## A permutation group challenge

Long ago, in the distant past before the Classification of Finite Simple Groups, Peter Neumann, Jan Saxl and I investigated the class of permutation groups acting on sets of even cardinality n = 2k, with the following interchange property: Any subset of … Continue reading

Posted in exposition, open problems
Tagged CFSG, homogeneity, permutation groups, semigroups
1 Comment