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# Category Archives: open problems

## Discrete mathematics in Derby

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

## The power graph yet again

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

## Circular repeated-measurements designs

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

## Random orbits on colourings, or nested Markov chains

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

Posted in exposition, open problems
Tagged graph colouring, Markov chain, orbits, random walk
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## Projective and polar spaces

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

Posted in history, open problems, the Web
Tagged Desargues' Theorem, LaTeX, LaTeX picture environment, Pappus' Theorem, plain TeX, polar spaces, projective spaces
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## Chains of semigroups

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

## A niggling problem

Preparing my talk for the Research Day, I was reminded of a problem I can’t solve, that has niggled me for many years. Maybe someone else can solve it, or maybe I will be encouraged to do it myself. Here … Continue reading

Posted in open problems
Tagged almost all quasigroups, Latin squares, loops, multiplication groups, quasigroups
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