Category Archives: exposition

a post aimed to teach something

A precious jewel

One of my favourite textbooks is Simmons’ Introduction to Topology and Modern Analysis. In the introduction, the author distinguishes two types of mathematics: the rare jewels, like the formula saying that the Riemann zeta function evaluated at 2 is π2/6; … Continue reading

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Matroids and polymatroids

Jack Edmonds’ LTCC intensive course is now over. It differed in several respects from what was advertised. First, he shared the presentation with Alex Fink on a roughly equal basis; second, bimatrix games were shelved in favour of some exciting … Continue reading

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Cayley digraphs and fractals

I have been thinking recently about the generation graph of a finite group: this is the graph whose vertices are the group elements, two vertices joined by an edge if together they generate the group. Of course the graph is … Continue reading

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June

This month, a beautiful formula on an old door panel in Prague. (It may not be very legible in this low-resolution copy.) The formula is for l(Sn), the length of the longest chain of subgroups in the symmetric group Sn. … Continue reading

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Scottish Combinatorics Meeting

At the end of April, I was at the first Scottish Combinatorics Meeting in Glasgow. The first day was somewhat overcast, but we were safely indoors in the Mathematics department: coffee, lunch and tea were provided in the common room. … Continue reading

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NBSAN in St Andrews

This week, during a spell of lovely spring weather and new blossom, the 20th meeting of the North British Semigroups and Applications Network was held in St Andrews, organised by Markus Pfeiffer. It was good to see old friends such … Continue reading

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Generating singular maps

Last week, Max Gadouleau and Alonso Castillo-Ramirez visited St Andrews. With James Mitchell, we worked on a problem about generating the semigroup of singular maps on a set (the full transformation semigroup minus the symmetric group). As usual in this … Continue reading

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