Category Archives: open problems

unsolved mathematical problems

A problem on diophantine approximation

Posted on 10/09/2012 by

Let n be a positive integer, and c a vector in Rn whose components are linearly independent over Q. Is it true that any line with direction vector c passes arbitrarily close to a point with integer coordinates? This is … Continue reading →

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Digital filters and bridge rankings

Posted on 23/05/2012 by

Shaun Bullett forwarded to me this request from Mike Christie. If anyone would like to collaborate on this, please contact Mike directly: his contact details are below. I have recently developed the method and software used by the English Bridge … Continue reading →

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London Combinatorics Colloquia

Posted on 18/05/2012 by

This week saw the two linked London Combinatorics Colloquia, at Queen Mary and the London School of Economics. Not so long ago, a one-day meeting in Reading organised by Anthony Hilton was a fixture of the calendar. When Anthony came … Continue reading →

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Counting colourings of graphs

Posted on 12/04/2012 by

Every graph theorist knows that the colourings of a graph with a given number of colourings are counted by a certain polynomial, the chromatic polynomial of the graph. My purpose here is to point out that there is more to … Continue reading →

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Permutation groups and regular semigroups, 2

Posted on 06/04/2012 by

João Araújo and I have been working together this week, and the paper, which I discussed here, is nearly ready to submit, after we managed a couple of quite significant improvements. I’d like to draw attention to a couple of … Continue reading →

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Automorphisms of groups

Posted on 05/11/2011 by

I set a question to my group theory class. It is quite easy until suddenly you find yourself falling off a cliff into deep water. Indeed, I don’t know the answer to the second part of this question. Show that … Continue reading →

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The Aitken lectures

Posted on 19/10/2011 by

Last Friday and this Monday we were visited by Geoff Whittle, the 2011 Aitken lecturer, sponsored by the London Mathematical Society. It was good for me to go some small way towards repaying Geoff’s hospitality when I was in Wellington … Continue reading →

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Remoteness

Posted on 11/10/2011 by

After the last bit of bureaucratic nonsense, what a relief to turn to mathematics again. Maximilien Gadouleau and I have just submitted a paper about a concept for finite metric spaces somewhat related to domination, which we call remoteness. It … Continue reading →

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Combinatorial representations

Posted on 30/08/2011 by

It is nice when several things that I care about come together. That is the story I have to tell here. Some history In April 2008, I visited New Zealand as the Forder Lecturer, a collaborative venture of the London … Continue reading →

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A card trick, 3

Posted on 22/08/2011 by

A double Youden rectangle is a set of size kn with two partitions into k sets of n and two into n sets of k satisfying the appropriate orthogonality and balance conditions as defined here: thus, two partitions of different … Continue reading →

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