Category Archives: open problems

unsolved mathematical problems

Graphs on groups, 5

Posted on 26/03/2021 by Peter Cameron

I gave two lectures on this stuff to a new research seminar on Groups and Graphs, run by Vijayakumar Ambat in Kochi, Kerala. The first was an introduction to the hierarchy, the second was about cographs and twin reduction, why … Continue reading →

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Graphs on groups, 4

Posted on 18/02/2021 by Peter Cameron

Here is a small problem, mixing group theory and number theory, which might appeal to someone. A couple of definitions. The power graph of a group G has an edge from x to y if one is a power of … Continue reading →

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Induced subgraphs of power and commuting graphs

Posted on 16/12/2020 by Peter Cameron

For those who like thinking about these things, here is a small observation and a few problems. As I have recently discussed, the power graph of a group is perfect. This means that all its induced subgraphs are perfect, and … Continue reading →

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Ramanujan+100

Posted on 15/12/2020 by Peter Cameron

I have just spent the last four days in Kochi, Kerala, at the International Conference on Number Theory and Discrete Mathematics, commemorating Srinivasa Ramanujan, the great Indian mathematician, on the 100th anniversary of his far-too-early death. The conference had perhaps … Continue reading →

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Oligomorphic groups: topology or geometry?

Posted on 10/12/2020 by Peter Cameron

One perhaps unexpected result of the pandemic is that there is a huge volume of really interesting mathematics flying around the internet at the moment, courtesy of Zoom and other platforms. This week I went to a talk by Joy … Continue reading →

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Between Fermat and Mersenne

Posted on 07/10/2020 by Peter Cameron

The following problem came up in something I was doing recently. I have no idea how difficult it is – it looks hard to me – but I would be glad to hear from anyone who knows more than I … Continue reading →

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Association schemes for diagonal groups

Posted on 12/05/2019 by Peter Cameron

Sean Eberhard commented on my posts on diagonal groups (see here and here). He is correct; there is an association scheme preserved by the full diagonal group with n factors in the socle; it is non-trivial if n > 2. The details … Continue reading →

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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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Kourovka Notebook, 19th edition

Posted on 22/04/2018 by Peter Cameron

The latest edition (the 19th) of the Kourovka Notebook has just been released. It now has its own website, https://kourovka-notebook.org/. The Kourovka Notebook has been going for more than 50 years, longer than my life as a mathematician. It is … Continue reading →

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Polynomially bounded orbit counts

Posted on 12/04/2018 by Peter Cameron

The best news I had yesterday was an email from Justine Falque with a link to a paper that she and Nicolas Thiéry have just put on the arXiv. The 12-page document is only the “short version”, and a longer … Continue reading →

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