Tag Archives: semigroups

All kinds of mathematics …

Posted on 11/12/2016 by

Please reserve the dates 24-27 July 2017 in your diary! Next year, I will turn 70. Some good friends (notably João Araújo) are arranging a conference in Lisbon to mark the occasion, and many other good friends have agreed to … Continue reading →

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Rainbows in the plane

Posted on 24/11/2016 by

As usual in Lisbon, I have been working with João Araújo on semigroups. But sometimes research has unusual spin-offs, such as the following curious fact: Fact If the points of a projective plane are coloured with four colours (all of … Continue reading →

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Partition homogeneity

Posted on 11/01/2016 by

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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12160

Posted on 27/10/2015 by

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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Generating singular maps

Posted on 12/04/2015 by

Last week, Max Gadouleau and Alonso Castillo-Ramirez visited St Andrews. With James Mitchell, we worked on a problem about generating the semigroup of singular maps on a set (the full transformation semigroup minus the symmetric group). As usual in this … Continue reading →

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Chains of semigroups

Posted on 27/01/2015 by

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 →

Posted in exposition, open problems, symmetric group | Tagged , , , , , , | 7 Comments

Subsets and partitions

Posted on 24/02/2014 by

There are several packing and covering problems for subsets of a set, which have been worked over by many people. For example, given t, k and n, how many k-subsets of an n-set can we pack so that no t-subset … Continue reading →

Posted in mathematics, open problems | Tagged , , , | 1 Comment