Shrikhande 100

Professor S. S. Shrikhande is 100. I offer him my warmest congratulations and birthday greetings.

Among much else in his distinguished career, he was one of the three who showed that a pair of orthogonal Latin squares exists for every order except 2 and 6, thus disproving a conjecture of Euler (who thought they would not exist for orders congruent to 2 mod 4). These three (Bose, Shrikhande and Parker) were dubbed the “Euler spoilers”. He also characterised the line graphs of regular complete bipartite graphs by their parameters as strongly regular graphs, apart from a unique exception on 16 vertices now called the Shrikhande graph. This led on to the work of Seidel and others on strongly regular graphs, and in particular to my own work with Goethals, Seidel and Shult on graphs with least eigenvalue −2 and their connection with root systems.

I discussed these two things and their relationship here.

You can find a tribute and account of the celebrations here.

About Peter Cameron

I count all the things that need to be counted.
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