Tag Archives: permutation groups

Real v recreational mathematics

Posted on 10/04/2014 by

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 →

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A thrifty algorithm

Posted on 20/01/2013 by

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 , , , , , | 4 Comments

A permutation group challenge, 2

Posted on 26/12/2012 by

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 →

Posted in open problems | Tagged , , | 1 Comment

A permutation group challenge

Posted on 19/12/2012 by

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 →

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Synchronizing coherent configurations

Posted on 23/08/2012 by

In previous posts I have discussed coherent configurations and synchronization. Yesterday I realised that these two topics can be combined … Synchronization A (finite-state, deterministic) automaton consists of a finite set of states and a finite set of transitions, each … Continue reading →

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Permutation groups and regular semigroups

Posted on 04/10/2011 by

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 →

Posted in exposition, mathematics | Tagged , | 5 Comments

MathOverflow

Posted on 05/08/2011 by

Today I put a toe into the pool that is MathOverflow for the first time. My question was: Which graphs have the property that the number of i-vertex induced subgraphs is at most i for some i<n/2 (where n is … Continue reading →

Posted in doing mathematics, mathematics | Tagged , , , | 7 Comments