Tag Archives: Thomas Kirkman

EKR, Steiner systems, association schemes, and all that

Posted on 29/09/2017 by

A great number of mathematical problems amount to looking in a large but highly structured graph, and finding a complete or null subgraph of largest possible size there. For a simple example, consider Latin squares of order n. One of … Continue reading →

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Steiner systems exist

Posted on 06/02/2014 by

A Steiner system S(t,k,n) is a collection of k-subsets (called “blocks”) of an n-set of “points” with the property that any t-set of points is contained in a unique block. To avoid trivial cases, we assume that t<k<n. Since the … Continue reading →

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Combinatorics, Algebra and More: conference report

Posted on 21/07/2013 by

I wrote about the walks already, but not about the conference itself. It was an amazingly friendly and good-natured event: everyone seemed to be happy and cheerful, the College catering staff excelled themselves (they even put on a cream tea … Continue reading →

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Kirkman’s schoolgirls and their friends

Posted on 01/06/2011 by

Often it happens that, when I think about a hard problem, I am absolutely convinced that I know what the answer will be, but I merely lack a proof. In this post I want to discuss a problem which I … Continue reading →

Posted in exposition, open problems | Tagged , , , , , | 5 Comments