Category Archives: exposition

a post aimed to teach something

The symmetric group, 13

Posted on 16/06/2013 by

In my post on the Novi Sad Algebraic Conference, I described how the symmetric group on a set X is “contained” in the full transformation semigroup on X, which is itself contained in the clone of functions on X. In … Continue reading →

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Algebra in Novi Sad

Posted on 09/06/2013 by

I have just spent a very wet week in Novi Sad at the fourth Novi Sad Algebraic Conference. Wet both in the sense of the large amount of rain that fell (most afternoons brought lightning, thunder and a heavy downpour) … Continue reading →

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London Combinatorics Colloquia, 2

Posted on 20/05/2013 by

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 →

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Finite geometry and probabilistic combinatorics

Posted on 05/05/2013 by

In the late 1960s, when I was born as a mathematician, I worked on finite permutation groups, on the edge of finite geometry and the combinatorics of very regular structures. I was dimly aware that there was a completely different … Continue reading →

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Endomorphism monoids of graphs

Posted on 25/04/2013 by

A monoid is, for me, a set of mappings on a finite domain which is closed under composition and contains the identity mapping. The composition is, of course, associative. Thus, it is “a group without the inverses”. A homomorphism from … Continue reading →

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Fibonacci numbers, 8

Posted on 06/03/2013 by

I am at the Southeastern Conference this week; I will say more about this later. Now, I simply want to add a post to my sequence on Fibonacci numbers, based on a lovely talk by Bruce Sagan. What I have … Continue reading →

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Two lectures

Posted on 03/03/2013 by

Last Friday I heard two very interesting lectures. One was the London Mathematical Society’s Mary Cartwright lecture, timed to coincide with the launch of a report by the LMS on good practice in supporting women in academic careers. It was … Continue reading →

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Primitivity

Posted on 27/02/2013 by

The first mathematics book that I read really seriously was Helmut Wielandt’s Finite Permutation Groups. So I have known the definition of a primitive permutation group for more than forty years. But there is still more to learn. My recent … Continue reading →

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Commuting graph, 2

Posted on 25/02/2013 by

Last week Chris Parker gave a very interesting talk in the London Algebra Colloquium on this topic. It is an excellent example of a curious phenomenon. If you look for your keys under the lamppost, then in a Borgesian way … Continue reading →

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The Graph Extension Theorem

Posted on 03/02/2013 by

I made some notes on the Graph Extension Theorem for a new research project. They may be of wider interest, so here is a summary. Shult’s Graph Extension Theorem is a simple device for showing that certain permutation groups have … Continue reading →

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