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Tag Archives: primitive groups
Automorphism groups of transformation semigroups
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
Posted in doing mathematics, open problems, Uncategorized
Tagged automorphism, primitive groups, synchronization
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Road closures and idempotentgenerated semigroups
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
9,21,27,45,81,153,…
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
Butterflies
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 nonpermutation f from this set to itself if the semigroup generated by G and … Continue reading
Easy to state, hard to solve?
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
Posted in exposition, open problems
Tagged graphs, homomorphisms, primitive groups, rigid graphs, switching classes, tournaments
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Automorphism groups of hypergraphs
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
Posted in exposition, mathematics
Tagged Akos Seress, hypergraphs, Laci Babai, Pablo Spiga, primitive groups
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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
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Primitive graphs
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 nontrivial equivalence relation which it preserves. This post is not about why primitive graphs … Continue reading