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# Tag Archives: Catalan numbers

## A week in Vienna

Last week, in the second week of Spring break in St Andrews, I was in Vienna, giving a course of lectures to the PhD students, at the invitation of Tomack Gilmore, a Queen Mary undergraduate now finishing his PhD with … 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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## Permutation patterns, day 1

Today is the first day of Permutation Patterns 15, at the London Mathematical Society headquarters in De Morgan House. Registration began at 8.30. I don’t like using the Underground at that time of day if it can be avoided; but … Continue reading

## Bijective proofs

A fourth proof Last month I described three proofs of the formula for the number of ways to choose k objects from a set of n, if repetition is allowed and order is not significant; it is the same as … Continue reading

Posted in exposition, open problems
Tagged bijections, Catalan numbers, Catalan objects, Dima Fon-Der-Flaass, permutations, sampling
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