Tag Archives: permutation groups

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

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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

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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

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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

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Synchronizing coherent configurations

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

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

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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

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Combinatorial Yang-Baxter

My paper with Tatiana Gateva-Ivanova is to be published. I’ll describe it here to demonstrate that one can find permutation groups almost anywhere. The Yang–Baxter equation (YBE) is a kind of braiding equation for a linear map R on V⊗V. … Continue reading

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