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# Category Archives: exposition

## Guessing numbers of graphs

A paper, “Guessing games on triangle-free graphs”, by Anh Dang, Søren Riis, and me, has just appeared in the Electronic Journal of Combinatorics. Here is a brief discussion of what it is about. It is always a pleasant surprise when … 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

## 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

Posted in exposition, history
Tagged homogeneity, partitions, semigroups, symmetric groups, transitivity
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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

## 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

## 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

Posted in events, exposition
Tagged asymptotically good codes, Bert Gerards, Charles Semple, delta-matroids, Dillon Mayhew, excluded minors, Geoff Whittle, independent sets in the Johnson graph, invariants, James Oxley, Jim Geelen, mereotopology, representable matroids, ribbon graphs, Rota's basis conjecture, Rota's conjecture
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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

Posted in exposition, open problems
Tagged graph colouring, Markov chain, orbits, random walk
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