Category Archives: open problems

unsolved mathematical problems

Problems

Posted on 12/09/2016 by

I have begun the long job of updating my collection of open problems. I would appreciate any help! My St Andrews problems are here, and are in pretty good shape (there are only 14 of them so this wasn’t a … Continue reading →

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Discrete mathematics in Derby

Posted on 23/03/2016 by

This week I have been at a conference on “Theoretical and Computational Discrete Mathematics” at the University of Derby, under the auspices of the Institute for Mathematics and its Applications. The University of Derby was founded as the Derby Diocesan … Continue reading →

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The power graph yet again

Posted on 15/03/2016 by

Five years ago, I posted a short update on the power graph of a group. Now, finally, the paper resulting from this has appeared on the arXiv; my coauthors are Ghodratollah Aalipour, Saieed Akbari, Reza Nikandish and Farzad Shaveisi. I … Continue reading →

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Circular repeated-measurements designs

Posted on 01/01/2016 by

My first paper in a real statistical journal has just been almost accepted (just a bit of re-formatting …) The paper is entitled “On optimality and construction of circular repeated-measurements designs”, the other authors are R. A. Bailey, K. Filipiak, J. Kunert and A. Markiewicz. … Continue reading →

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Random orbits on colourings, or nested Markov chains

Posted on 15/12/2015 by

I promised after reporting Catherine Greenhill’s talk last week that I would advertise this little problem; so here goes. How do we pick a random proper colouring of a graph Γ? There is a simple Markov chain for this, also … Continue reading →

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Projective and polar spaces

Posted on 04/04/2015 by

I have produced a new edition of my lecture notes on Projective and Polar Spaces and put them with my lecture note collection. I did this because it seems that people still find some use for these notes. According to … Continue reading →

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Chains of semigroups

Posted on 27/01/2015 by

I have written here about the lovely formula for the length of the longest chain of subgroups in the symmetric group Sn: take n, increase it by 50% (rounding up if necessary), subtract the number of ones in the base … Continue reading →

Posted in exposition, open problems, symmetric group | Tagged , , , , , , | 7 Comments