Tag Archives: formal power series

A challenge

Let a(n) be defined in the following manner. Write n as an ordered sum of positive integers in all possible ways. (The number of such expressions is 2n−1; showing this is a pleasant exercise, but it is not relevant for … Continue reading

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Advanced Combinatorics: the St Andrews lectures

Three years ago, when I joined the School of Mathematics and Statistics at the University of St Andrews, it was suggested that I might like to give a final year MMath module on “Advanced Combinatorics”. No compulsion. Well, of course … Continue reading

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Categorification, step 1

Today at the St Petersburg meeting, Igor Frenkel talked about categorification. He explained that there are five levels (maybe more!) and one has to take certain steps between them; he illustrated with an example, where level 0 was Jacobi’s Triple … Continue reading

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Combinatorics in Scotland, group theory in Portugal

I never really wanted to retire. For various reasons which no longer matter, I decided to retire from my position at Queen Mary, University of London, on turning 65 two years ago. I hoped that I would find enough to … Continue reading

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LTCC course finished

Yesterday was the last day of my LTCC course on Enumerative Combinatorics. Thanks to the students who stuck it out to the end. I produced notes week by week and now you can find the complete notes on this site. … Continue reading

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Fibonacci numbers, 3

The Fibonacci recurrence, an = an−1+an−2 is linear. This might suggest either of two things to you, depending on your background: Like a linear differential equation, its solutions obey the superposition principle; the sum of solutions is a solution, and a multiple … Continue reading

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