Shartchandra Shankar Shrikhande

Shartchandra Shankar Shrikhande, IMS Fellow and well known combinatorial mathematician, passed away on April 21 at his residence in India. He was 102.

S.S. Shrikhande was born in Sagar, India, on October 19, 1917. Having won scholarships, he was able to complete his BSc Honours at the Government College of Science (now known as the Institute of Science) in Nagpur with a first rank and a gold medal. He went on to receive his doctoral degree on Construction of Partially Balanced Designs from the University of North Carolina in 1950, under the supervision of Raj Chandra Bose. Prior to that, he was a Research Fellow at the Indian Statistical Institute. Professor Shrikhande, R.C. Bose and E. T. Parker jointly disproved Euler’s 1782 conjecture that mutually orthogonal Latin squares cannot exist for orders of the form 4n+2 for any n. This was proved by Euler himself for n=0 and by Gaston Tarry in 1901 for n=1. The first analytical counterexample was found by Bose and Shrikhande in early 1959 for n=5. Later the same year, Bose, Shrikhande and Parker proved the general result that in fact such orthogonal squares exist for all orders 4n+2 except n=0,1. The trio were dubbed “Euler’s Spoilers”—as reported in the front-page New York Times article on April 26, 1959.

Dr. Shrikhande also gave a remarkable construction of a special strongly regular Cayley graph with each pair of vertices having exactly the same number of neighbors and each vertex having exactly the same degree. This graph, now known as the Shrikhande graph has found many applications in design of experiments.

Professor Shrikhande was the founding Head of the mathematics department at Bombay University and the founding Director of the Center for Advanced Study, Bombay. Professor Shrikhande is survived by his sons Mohan (who is a professor of mathematics at the Central Michigan University) and Anil, and a daughter, Asha; his wife Shakuntala passed away in 1987.

Written by B.V. Rao and Anirban DasGupta