Sharadchandra Shankar Shrikhande

Shrikhande graph

Sharadchandra Shankar Shrikhande (often cited as SS Shrikhande ; born October 19, 1917 in Sagar , Central Provinces [now Madhya Pradesh ]; † April 21, 2020 in Vijayawada , Andhra Pradesh ) was an Indian mathematician .

Life

Shrikhande came from a middle class family. He studied at Nagpur University with a bachelor's degree in 1939 and taught statistics and mathematics there from 1942 to 1958. As early as the 1940s he made several long trips to meet Raj Chandra Bose in Calcutta and went to the University of North Carolina to do his doctorate in 1950 (Construction of partially balanced designs and related problems). They then worked closely together until Bose's death. 1951 Shrikhande Assistant Professor at the University of Kansas at Lawrence and 1958 to 1960 Associate Professor at the University of North Carolina at Bose. In 1960 he became a professor at Banaras Hindu University and in 1963 professor and head of the mathematics faculty at the University of Bombay . He was also director of the Center for Advanced Study in Mathematics in Bombay. In 1978 he retired. 1983-1986 he was director of Mehta Research Institute in Allahabad .

He became known when he and Raj Chandra Bose refuted Euler's Conjecture ( Leonhard Euler 1782) that no orthogonal Latin squares of the order exist (they found a counterexample to the conjecture for n = 22). Your Latin square was shown on the cover of Scientific American in November 1959. Almost at the same time Ernest Tilden Parker (1926–1991) found a counterexample for n = 10 in the USA. This led to a joint work with Shrikhande and Bose in 1960, in which they showed that orthogonal Latin squares exist for all orders . ${\displaystyle n=4k+2}$ ${\displaystyle n\geq 10}$

He is also known for designs in test planning. The Shrikhande graph is named after him and was discovered by him in 1959, a strongly regular graph with 16 nodes and 48 edges, in which every node has degree 6. Each pair of nodes (whether connected or not) has exactly two other nodes as neighbors.

He was a member of the Indian National Science Academy, the Indian Academy of Sciences , the Institute of Mathematical Statistics, and the International Statistical Institute. Shrikhande was visiting professor at the University of Wisconsin , Ohio State University , State University of New York , Stanford University, and Colorado State University . He was also associated with the Indian Statistical Institute in various functions .

His son Mohan Shrikhande is a professor of combinatorics at Central Michigan University .

literature

• Editorial: SS Shrikhande and his work. An appreciation, Journal of Statistical Planing and Inference, Volume 95, 2001, pp. 3-7
• Selected Papers of SS Shrikhande, 2 volumes, ed. DS Meek, RG Stanton, Charles Babbage Research Center, Winnipeg 1985

Individual evidence

1. ↑ Sharadchandra Shankar Shrikhande: Obituary. In: news18.com/news/opinion , accessed on May 11, 2020.
2. ↑ Sharadchandra Shankar Shrikhande in the Mathematics Genealogy Project (English)
3. ↑ RC Bose, SS Shrikhande: On the falsity of Euler's conjecture about the non-existence of two orthogonal latin squares of order 4t + 2 . In: Proc. Nat. Acad. Sci. USA . tape 45 , 1959, pp. 734-737 , PMID 16590435 , PMC 222625 (free full text) - (English).
4. ↑ RC Bose and SS Shrikhande: On the construction of sets of mutually orthogonal latin squares and the falsity of a conjecture of Euler . In: Trans. Amer. Math. Soc . tape 95 , 1960, pp. 191-209 , doi : 10.1090 / S0002-9947-1960-0111695-3 (English).
5. ↑ RC Bose, SS Shrikhande, ET Parker: Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler's conjecture . In: Canadian Journal of Mathematics . tape 12 , 1960, pp. 189– , doi : 10.4153 / CJM-1960-016-5 (English, PDF ).
6. ^ Shrikhande, SS: The Uniqueness of the Association Scheme ${\displaystyle L_{2}}$ . In: Ann. Math. Stat. tape 30 , 1959, pp. 781-798 , JSTOR : 2237417 (English).
7. ↑ Eric Weisstein, Shrikhande Graph