Category Archives: open problems

unsolved mathematical problems

Kourovka Notebook, 19th edition

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

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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A problem

Since I have been saying rather a lot about association schemes and coherent configurations lately, I thought I would mention an open problem. This is probably one for the experts, and I guess it has been ignored because of the … Continue reading

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Outer automorphisms

I have just put on the arXiv a paper I wrote with Sam Tarzi ten years ago. I want to say here something about the context, the contents of the paper, and the reason for posting it now. Outer automorphisms … Continue reading

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A small fact about the Petersen graph

The Petersen graph has 10 vertices and 15 edges, and the complete graph on 10 vertices has 45 edges. However, Allen Schwenk and (independently) O. P. Lossers (Jack van Lint’s problem-solving seminar in Eindhoven) showed that you can’t partition the … Continue reading

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Algebraic properties of chromatic polynomials, 2

My paper with Kerri Morgan on algebraic properties of chromatic roots (described here) has just appeared in the Electronic Journal of Combinatorics: you can find it here. I won’t say any more about it, except to pose a challenge which … Continue reading

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Automorphism groups of transformation semigroups

I have been in the transformation semigroups game for nearly ten years now, but I still feel that I am finding my feet. Here is apparently a huge difference between permutation groups and transformation semigroups, one which is still not … Continue reading

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