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# Category Archives: exposition

## Road closures and idempotent-generated 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

## Rainbows in the plane

As usual in Lisbon, I have been working with João Araújo on semigroups. But sometimes research has unusual spin-offs, such as the following curious fact: Fact If the points of a projective plane are coloured with four colours (all of … Continue reading

## Imprimitive permutations in primitive groups

Asymptotics of permutation counts is a subject with a long history. The result that the proportion of permutations which are derangements (that is, have no fixed points) is very close to 1/e is one of the oldest results in enumerative … Continue reading

Posted in exposition
Tagged imprimitive, permutation, permutation group, primitive, Wielandt's conjecture
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## Curves

Just back from an enjoyable evening at Gresham College, where Jan van Maanen from Utrecht gave the BSHM–Gresham lecture marking the tercentenary of the death of Leibniz next month, preceded by warm-up acts by Snezana Lawrence and my colleague Kenneth … Continue reading

## Algebraic properties of chromatic roots

It has been a long time coming. I wrote back in 2011 about the work Kerri Morgan and I were doing on algebraic properties of chromatic roots. A paper has just gone on the arXiv. I will just recap here, … Continue reading

## Perth, week 3

The black swan is the emblem of Western Australia – but it seems a little odd that, on the State coat of arms, there is a picture of one being cooked in a large pot of water by two kangaroos … Continue reading

Posted in events, exposition, geography
Tagged Agrawal's conjecture, black swan, finite geometry, flow polynomials
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