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# Tag Archives: synchronization

## The Hall–Paige conjecture

A Latin square of ordern is an n×n array of symbols from an alphabet of size n with the property that each symbol in the alphabet occurs once in each row or column. Two Latin squares L and M are … Continue reading

## RA position in St Andrews

We are looking for a postdoctoral research assistant on the project “Bi-synchronizing automata, outer automorphism groups of Higman–Thompson groups, and automorphisms of the shift”. The Principal Investigator is Collin Bleak; I am the co-I. The project involves an interesting mix … Continue reading

## Synchronization and all that, 2

The story I told in the last post is not over. The recent development is that we spotted a mistake in the paper. An easy mistake to make: we had simply used the symbol n in two different places with … Continue reading

Posted in doing mathematics, exposition
Tagged association scheme, large sets, ovoid, Philippe Delsarte, quadric, spread, Steiner systems, synchronization, triality
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## Synchronization and separation in the Johnson schemes

Today a paper by Mohammed Aljohani, John Bamberg and me went on the arXiv on this topic. Here is a brief summary of what it is about. Synchronization comes in several flavours, and the point of the paper is to … Continue reading

Posted in exposition, Uncategorized
Tagged association scheme, Peter Keevash, Philippe Delsarte, separation, synchronization
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## A week in Vienna

Last week, in the second week of Spring break in St Andrews, I was in Vienna, giving a course of lectures to the PhD students, at the invitation of Tomack Gilmore, a Queen Mary undergraduate now finishing his PhD with … Continue reading

## 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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## The Higman–Thompson groups

I celebrated the last day of spring last week with the appearance of two substantial papers on the arXiv: one with Maria Elisa Fernandes, Dimitri Leemans, and Mark Mixer, proving that the maximum rank of a regular polytope whose group … Continue reading

Posted in exposition
Tagged automata, Cantor space, Grtaham Higman, homeomorphisms, regular polytopes, Richard Thompson, synchronization, transducers
7 Comments

## ACCMCC, Days 4 and 5

Penny Haxell opened proceedings on Thursday with her astonishing work with Ron Aharoni. They give a sufficient condition for a tripartite 3-uniform hypergraph (one whose vertex set is partitioned into three parts so that each hyperedge contains one vertex from … Continue reading

Posted in events
Tagged affine planes, Latin squares, Markov chains, switching, synchronization, transversals, Tutte polynomial
1 Comment

## Permutation groups and transformation semigroups

When I first decided to apply to the LMS to run a Durham symposium on Permutation Groups and Transformation Semigroups, I had a fairly clear idea of what I wanted: topics (both finite and infinite) where the techniques and results … Continue reading

## 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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