Category Archives: mathematics

Graphs on groups, 13

Posted on 05/02/2022 by Peter Cameron

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 →

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Graphs on groups, 2

Posted on 27/01/2021 by Peter Cameron

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 →

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Graphs defined on groups

Posted on 23/01/2021 by Peter Cameron

I’ve been spending time I can ill afford on various questions related to graphs whose vertex set is a group G and which capture some of the structure of G. (I interpret this to mean that the graph is invariant … Continue reading →

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Family

Posted on 19/01/2021 by Peter Cameron

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 →

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Memories of Peter Neumann

Posted on 24/12/2020 by Peter Cameron

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 →

Posted in history, mathematics, the LMS | Tagged | 9 Comments

Fair games and Artin’s conjecture

Posted on 10/04/2019 by Peter Cameron

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 →

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The Hall–Paige conjecture

Posted on 18/12/2018 by Peter Cameron

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 …

Posted on 11/12/2016 by Peter Cameron

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

Posted on 06/06/2016 by Peter Cameron

Recently, I discussed Olexandr 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), Olexandr raised … Continue reading →

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Guessing numbers of graphs

Posted on 20/03/2016 by Peter Cameron

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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