Category Archives: mathematics

The Hall–Paige conjecture

A Latin square of ordern is an n×n array of symbols from an alphabet of size n with the property that each symbol in the alphabet occurs once in each row or column. Two Latin squares L and M are … Continue reading

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All kinds of mathematics …

Please reserve the dates 24-27 July 2017 in your diary! Next year, I will turn 70. Some good friends (notably João Araújo) are arranging a conference in Lisbon to mark the occasion, and many other good friends have agreed to … Continue reading

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Group names

Recently, I discussed Alexander Konovalov’s crowd-sourced project to verify and extend the known values of the function gnu(n), the number of groups of order n. A month and a half ago (but I have only just noticed it), Alexander raised … Continue reading

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Guessing numbers of graphs

A paper, “Guessing games on triangle-free graphs”, by Anh Dang, Søren Riis, and me, has just appeared in the Electronic Journal of Combinatorics. Here is a brief discussion of what it is about. It is always a pleasant surprise when … Continue reading

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Sharing pizza

I was in Bristol last week, where people were discussing the following problem over drinks and dinner following my talk. I hope they don’t mind my publicising a nice problem. I will tell you nothing about the solution, but I … Continue reading

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Auckland

Rosemary and I are in Auckland on a seven week research visit, supported by Hood fellowships from the University. Already I am working on several projects, on polytopes, automorphic loops, symmetric designs, optimal neighbour designs, and median graphs. I hope … Continue reading

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Primitive switching classes

Last year I wrote here about switching classes of graphs for which the switching class has a primitive automorphism group. (I repeat the definitions briefly below.) I conjectured that, except for the trivial switching classes of the complete and null … Continue reading

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