Tag Archives: primitive groups

Automorphism groups of transformation semigroups

Posted on 18/01/2017 by

I have been in the transformation semigroups game for nearly ten years now, but I still feel that I am finding my feet. Here is apparently a huge difference between permutation groups and transformation semigroups, one which is still not … Continue reading →

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Road closures and idempotent-generated semigroups

Posted on 28/11/2016 by

The University of St Andrews is installing a biomass boiler, to provide hot water to heat University buildings, on the old paper mill site at Guardbridge. The water has to be piped four miles to St Andrews, and this big … Continue reading →

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9,21,27,45,81,153,…

Posted on 16/10/2014 by

This is the sequence of degrees of primitive groups which don’t synchronize a map of rank 3, equivalently graphs with clique number and chromatic number 3 having primitive automorphism groups. You could argue that the sequence should start with 3, … Continue reading →

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Butterflies

Posted on 14/10/2014 by

I am in Lisbon working with João Araújo and Wolfram Bentz on synchronization. We say that a permutation group G on the set {1,…n} synchronizes a non-permutation f from this set to itself if the semigroup generated by G and … Continue reading →

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Easy to state, hard to solve?

Posted on 31/07/2014 by

I described here how Pablo Spiga and I showed that all but finitely many nontrivial switching classes of graphs with primitive automorphism group contain a graph with trivial automorphism group, and found the six exceptions. (The trivial switching classes are … Continue reading →

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Automorphism groups of hypergraphs

Posted on 01/07/2014 by

I am getting old and forgetful, but I don’t think I said anything here about this problem yet. If I did, apologies for the repetition – but there is something new to report! In April, Laci Babai and I finally … 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 →

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Primitive graphs

Posted on 11/01/2013 by

A primitive graph is one whose automorphism group acts primitively on the vertices: that is, the group is transitive on the vertices, and there is no non-trivial equivalence relation which it preserves. This post is not about why primitive graphs … Continue reading →

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