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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
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
Posted in Lecture notes
Tagged Catalan numbers, chromatic polynomial, cycle index, doocot principle, enumeration, formal power series, Friendship Theorem, Gaussian coefficients, generalised line graphs, generalised quadrangles, IBIS groups, line graphs, Mathieu groups, matroid, Moebius inversion, orbit-counting lemma, projective planes, root systems, strongly regular graphs, symmetric Sudoku, triangle property, Tutte polynomial, weight enumerator
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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
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
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
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
