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# Tag Archives: primitive groups

## 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 non-permutation 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 non-trivial equivalence relation which it preserves. This post is not about why primitive graphs … Continue reading