Tag Archives: partitions

The geometry of diagonal groups

Posted on 18/04/2020 by Peter Cameron

This is an interim report on ongoing work with Rosemary Bailey, Cheryl Praeger and Csaba Schneider. We have reached a point where we have a nice theorem, even though there is still a lot more to do before the project … Continue reading →

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A family of non-synchronizing groups

Posted on 06/01/2019 by Peter Cameron

As I explained recently, according to the O’Nan–Scott Theorem, a finite primitive permutation group either preserves a Cartesian structure, or is of affine, diagonal or almost simple type. In all these types except the last, the action of the group … Continue reading →

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The existential transversal property

Posted on 21/08/2018 by Peter Cameron

One of the first things that João Araújo introduced me to when we started collaborating, after synchronization, was the universal transversal property: a permutation group G on the set {1,…,n} has the k-universal transversal property (k-ut for short) if, given … Continue reading →

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A puzzle for you

Posted on 09/04/2016 by Peter Cameron

The Petersen graph is perhaps the most famous graph of all. It has ten vertices, fifteen edges, valency 3, and no triangles. Since the complete graph on ten vertices has 45 edges and valency 9, one might ask whether the … Continue reading →

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Partition homogeneity

Posted on 11/01/2016 by Peter Cameron

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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G. C. Steward lectures 2008

Posted on 05/04/2015 by Peter Cameron

While I was uploading lecture notes, I also put on the page the notes from my G. C. Steward lectures at Gonville and Caius College in 2008. You can find them here. I spent the first half of 2008 in … Continue reading →

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A cliff

Posted on 06/08/2014 by Peter Cameron

The “combinatorial explosion” is a well-known phenomenon. I recently came across a very dramatic example of it. I was trying to compute the function F(n,k), defined to be the maximum of |S|×|P|, over all sets S of k-subsets and all … Continue reading →

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Combinatorics Ancient and Modern

Posted on 28/06/2013 by Peter Cameron

Towards the end of 2011, I posted a paper on the arXiv with the title “Aftermath”. A correspondent wondered if this was a Borgesian game, the final chapter to a nonexistent book. Happily, it was not so. Combinatorics Ancient and … Continue reading →

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