Tag Archives: Steiner system

From M12 to M24

On 20 January 2015, Paul Hjelmstad posted the following question on the GAP forum: Is there an easy way to generate a Steiner system S(5,8,24) for the Mathieu Group M24, if a Steiner system S(5,6,12) for the Mathieu Group M12 … Continue reading

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Steiner systems exist

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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Symmetry versus regularity

In my report on CAMconf, I didn’t mention Laci Babai’s talk, whose title was the same as that of this post. This was a talk that needed some thinking about. I want to describe the situation briefly, and then pose … Continue reading

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Kirkman’s schoolgirls and their friends

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