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# Tag Archives: graph endomorphisms

## A paper on synchronization

A paper on synchronization, written with João Araújo, Wolfram Bentz, Gordon Royle and Artur Schaefer, has just appeared on the arXiv. It is quite a substantial paper, and goes well beyond anything we have published (or that I have written … Continue reading

Posted in exposition
Tagged graph endomorphisms, primitive permutation groups, synchronization
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## Orbital combinatorics

Yesterday I went to Edinburgh to give a colloquium talk about synchronization, including the recent stuff about butterflies. The day before, I had discussed Artur Schäfer’s work with him, and he expressed a hope that if he went to the … Continue reading

## Random synchronization

Mikhail Berlinkov posted a paper on the arXiv this week proving that two random transformations of an n-set generate a synchronizing semigroup with probability 1-o(1/n) for large n. His approach was quite different from the one I’d been taking, using … Continue reading

Posted in mathematics, open problems
Tagged graph endomorphisms, random transformations, synchronization
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