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# Tag Archives: root systems

## Aliens Do Exist

The people from the planet Ade have intercepted radio transmissions from Earth, and have discovered that we know about the Petersen graph and the root system E6. One day, a flying saucer from Ade arrives on Earth and delivers an … Continue reading

Posted in doing mathematics, events
Tagged Petersen graph, random graph, root systems, Sira Gratz, University of Leeds
1 Comment

## British Mathematical Colloquium, day 2

Things may be a bit briefer from now on. The first plenary talk was by Irit Dinur on the unique games conjecture. I think I understood roughly what this conjecture says, but what it has to do with games, unique … Continue reading

## All kinds of mathematics: workshop and conclusion

The final day of the conference was devoted to a satellite workshop on “Symmetry in finite and infinite structures”. The morning was a solo performance by Laci Babai, in which he explained in detail his quasi-polynomial algorithm for graph isomorphism. … Continue reading

## The ADE affair, 6

Earlier this semester, we had a beautiful seminar by Pierre-Philippe Dechant, whose work has thrown some entirely new light on this beautiful work of art. I would like to explain a bit about this here. For more details, see his … 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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## An LMS meeting

Last Friday I went to the London Mathematical Society general meeting, at the BMA building in Tavistock Square. On a beautiful warm day I walked along the Regents Canal to Islington and then down through back streets past the former … Continue reading

## G. C. Steward lectures 2008

While I was uploading lecture notes, I also put on the page the notes from my G. C. Steward lectures at Gonville and Caius College in 2008. You can find them here. I spent the first half of 2008 in … Continue reading

Posted in history, Lecture notes, Neill Cameron artwork
Tagged automata, bagali polo, Euler, Latin squares, line graphs, magic squares, Moebius inversion, OEIS, On-line Encyclopedia of Integer Sequences, parking functions, partitions, root systems, statistics, Sudoku, synchronization, Tehran
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## Precursors

Jorge Luis Borges is one of the most mathematical of great writers. In an essay entitled “Kafka and his Precursors”, he pointed out that there is a strange collection of pieces and fragments, including Zeno’s paradox and stories by Han … Continue reading

## The ADE affair, 5

A root system is a finite set S of vectors in Euclidean space with the properties If s,λs∈S, then λ=±1. The set S is mapped to itself by the reflection in the hyperplane perpendicular to each element s of S. … Continue reading

Posted in exposition
Tagged Coxeter group, generalized line graphs, line graph, root systems, Whitney's theorem
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## The ADE affair, 4

Here is a cautionary tale to show that not everything that looks like an instance of the ADE classification actually is so. When I first learned about optimal design in statistics, I was very excited to find that there are … Continue reading

Posted in exposition
Tagged Ching-Shui Cheng, concurrence, Laplacian eigenvalues, optimal design, root systems, statistics
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