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Tag Archives: Cayley graphs
Graphs on groups, 3
Since this stuff keeps growing, I have decided to keep the most recent version on the web. It is now nearly twice as long as the first version I circulated. If you are interested, please take a copy: it’s at … Continue reading
G2D2, 2: first week
The campus of the China Three Gorges Hotel has a small river, full of waterlilies and lotus flowers. Beside it runs a main road, along which big water trucks run, shooting atomised water from cannon-like structures; we are told this … Continue reading
Normal
There are various overused terms in mathematics. “Normal” is one of them. Perhaps the four commonest uses are the following: A complex square matrix is normal if it commutes with its conjugate transpose. Normal matrices are precisely the ones which … Continue reading
Posted in exposition
Tagged Cayley graphs, field extensions, groups, matrices, terminology, topological spaces
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A Cayley graph challenge
Greg Cherlin showed that Henson’s graphs are Cayley graphs, so perhaps it is time to look again at the question: Is Covington’s graph a Cayley graph? Here, to start things off, is a simple fact: Covington’s graph G is not … Continue reading
The sound of problems falling
This month brought news that two problems I posed have been solved. A conjecture of mine was proved by Martin Bridson and Henry Wilton, and another question (which I didn’t feel brave enough to connjecture) has been answered by Greg … Continue reading
London Combinatorics Colloquia, 2
It’s that time of year again, and while I miss the buttercups in Reading, we had as usual a feast of interesting mathematics and a large and enthusiastic audience. It was a bit more tightly focussed than I would have … Continue reading
Posted in events, exposition
Tagged amenability, Ben Green, Cayley graphs, Endre Szemeredi, Gabor Kun, Noga Alon, Norman Biggs, Regularity Lemma, sum-free sets
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