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Category Archives: mathematics
Graphs on groups, 13
There are many results about the universality, or otherwise, of various graphs defined on groups: answers to questions of the form “for which graphs Γ is there a group G such that Γ is isomorphic to an induced subgraph of … Continue reading
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 2427 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 Olexandr Konovalov’s crowdsourced 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), Olexandr raised … Continue reading
Posted in mathematics
Tagged dihedral groups, Olexandr Konovalov, symmetric groups, unitary groups
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Guessing numbers of graphs
A paper, “Guessing games on trianglefree 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