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# Category Archives: doing mathematics

## The geometry of diagonal groups

This is an interim report on ongoing work with Rosemary Bailey, Cheryl Praeger and Csaba Schneider. We have reached a point where we have a nice theorem, even though there is still a lot more to do before the project … Continue reading

Posted in doing mathematics, exposition
Tagged Cartesian lattices, diagonal groups, partitions
3 Comments

## More on derangements

Francis Bacon, in The New Organon, developed a famous metaphor: Those who have handled sciences have been either men of experiment or men of dogmas. The men of experiment are like the ant, they only collect and use; the reasoners … Continue reading

## Au revoir, GRA

Today (Wednesday 18 March) the Groups, Representations and Applicatons programme at the Isaac Newton Institute came to a premature end. There are still some hopes that it can be revived later, but at the moment the only certainty is that … Continue reading

Posted in doing mathematics, symmetric group
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## Research trips in February

I don’t know how things have got so busy. I had two interesting trips in February; I worked hard, and some interesting mathematics resulted; but I don’t seem to have found the time to describe it. So here goes. This … Continue reading

## Aliens Do Exist

The people from the planet Ade have intercepted radio transmissions from Earth, and have discovered that we know about the Petersen graph and the root system E6. One day, a flying saucer from Ade arrives on Earth and delivers an … Continue reading

Posted in doing mathematics, events
Tagged Petersen graph, random graph, root systems, Sira Gratz, University of Leeds
1 Comment

## 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

## Kourovka Notebook, 19th edition

The latest edition (the 19th) of the Kourovka Notebook has just been released. It now has its own website, https://kourovka-notebook.org/. The Kourovka Notebook has been going for more than 50 years, longer than my life as a mathematician. It is … Continue reading

Posted in doing mathematics, history, open problems
Tagged identical relations, Kourovka Notebook, open problems
1 Comment

## Mathematical collaboration

I have just spent an entire weekend at a workshop on mathematical collaboration. It blew a huge hole in the time that I had to get on with urgent work that needs to be done, but it was such a … Continue reading

Posted in doing mathematics, events
Tagged collaboration, experimental philosophy, Fenner Tanswell, Josh Habgood-Coote, Paul Erdős, virtue theory
1 Comment

## Another Cameron–Erdős problem solved

In 1990, Paul Erdős and I published a paper on the topic of counting subsets of the first n natural numbers satisfying some restriction. The case we worked hardest on, and which attracted the most interest (it has its own … Continue reading

Posted in doing mathematics, Uncategorized
Tagged Cameron--Erdos, forbidding divisibility
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## Integrals of groups

Everyone who has studied mathematics knows what the derivative and integral of a function are. The derivative measures rate of change, the integral (the inverse operation) measures area under a curve. They are inverse operations; and two functions have the … Continue reading

Posted in doing mathematics, exposition
Tagged abelian group, derived subgroup, Frattini subgroup, inverse group theory
2 Comments