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# Category Archives: mathematics

## Fair games and Artin’s conjecture

A few years ago I described Persi Diaconis’ response to G. H. Hardy’s claim that there is a real dividing line between real and recreational mathematics. (See the report here.) This led from Persi’s first experiments in card shuffling to Artin’s conjecture … Continue reading

## 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

## 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

## 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

Posted in mathematics
Tagged Alexander Konovalov, dihedral groups, symmetric groups, unitary groups
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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

## 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

## 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

## 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

Posted in exposition, mathematics
Tagged Akos Seress, Don Taylor, Pablo Spiga, primitive group, switching class, two-graph
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## Automorphism groups of hypergraphs

I am getting old and forgetful, but I don’t think I said anything here about this problem yet. If I did, apologies for the repetition – but there is something new to report! In April, Laci Babai and I finally … Continue reading

Posted in exposition, mathematics
Tagged Akos Seress, hypergraphs, Laci Babai, Pablo Spiga, primitive groups
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## Busy times, 9: Beyond the limit in St Petersburg

Anatoly Vershik is a universal mathematician, with influential work in asymptotic combinatorics, groups and group actions, probability, mathematical physics, and many other areas. This week, I was in St Petersburg for a conference with the wonderful title “Representations, Dynamics, Combinatorics: … Continue reading

Posted in events, exposition, mathematics
Tagged Anatoly Vershik, asymptotic combinatorics, Ramsey theory, St Petersburg, string theory
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