Category Archives: exposition

a post aimed to teach something

Partition homogeneity

This post discusses a paper by Jorge André, João Araújo and me, which has just been accepted for the Journal of Algebra. There is a slight tangle to the history of this paper, which I want to describe. First a … Continue reading

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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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Cycles and trees

The cycle has taken us up through forests … Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance Here is a little nugget, and a problem. Nothing new but it might entertain you. Every permutation is a product of … Continue reading

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Conference for Geoff Whittle

In 2013, when I retired from Queen Mary (my first, unsuccessful, attempt at retiring), Geoff Whittle came and spoke at the conference my colleagues organised for me. He is also someone who has appeared on these pages a few times. … 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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The synchronizing monster

Today, a long paper on synchronizing groups (108 pages), by João Araújo, Ben Steinberg, and me, appears on the arXiv. It has been a long time coming. To quote from a post of mine in 2010, I became involved in … Continue reading

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12160 is an interesting number; but I didn’t know that until last night. As part of the work on semigroups, we are looking at the following problem. Given n and k, with n ≥ 2k, suppose that G is a k-homogeneous subgroup … Continue reading

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