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# Category Archives: mathematics

## Graphs on groups, 2

I wrote the long post about this to try to write it out of my system. No luck … I mentioned in that survey that every finite graph is embeddable as induced subgraph in the enhanced power graph, deep commuting … Continue reading

Posted in doing mathematics, mathematics
Tagged commuting graph, enhanced power graph
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## Family

The coincidence of Peter Neumann’s funeral and Eric Lander’s elevation in the last few days has inevitably made me think about family (in the mathematical sense). First, pictures of my aunts and uncles, brothers and sisters, sons and daughters, taken … Continue reading

## Memories of Peter Neumann

What follows are memories, and at my age my memory is not totally reliable, so don’t take any of this as absolute truth. But it is important to say that Peter was one of the kindest people. I owe him … Continue reading

## 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