Tag Archives: strongly regular graph

A request

In 1956, Helmut Wielandt proved that a primitive permutation group whose degree is twice a prime p is doubly transitive, unless p has the form 2a2+2a+1, in which case the group has rank 3, and its subdegrees are a(2a+1) and … Continue reading

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There is no McLaughlin geometry

Congratulations to Patric Östergård and Leonard Soicher, who have just completed a big computation whose conclusion is “There is no McLaughlin geometry”. The run-time of the computation was about 250 core-years. So what did they compute, and why does it … 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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The prehistory of the Higman-Sims graph

Triangle-free strongly regular graphs form a fascinating byway of combinatorics. These are regular graphs of valency k on v vertices, which contain no triangles, and have the property that any two non-adjacent vertices have μ common neighbours. The numbers (v,k,μ) … Continue reading

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Team games, 3

Recall the general problem: Given n players, arrange a series of matches, each between two teams of k players, in such a way that every pair of players are on the same team in s matches and on opposite teams … Continue reading

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