Category Archives: open problems

unsolved mathematical problems

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

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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

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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

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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

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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

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Bijective proofs

A fourth proof Last month I described three proofs of the formula for the number of ways to choose k objects from a set of n, if repetition is allowed and order is not significant; it is the same as … Continue reading

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Three versus four

The title is homage to the Gödel’s Last Letter and P=NP blog, which a week ago had a post entitled Two versus three. At the problem session at the Banff meeting last night, Dugald Macpherson and Andras Pongracz posed various … Continue reading

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