1994 Hall Medal awarded to Chris Rodger

 From BICA (15) 1995:

The 1995 Hall Medals of the ICA

The Hall Medals of the ICA are awarded to Fellows of the Institute who have not passed age 40 and who have already produced a distinguished corpus of significant research work. The Hall Medals were inaugurated in 1994, and the 1995 Hall Medals, the first to be granted, have been awarded to Ortrud Ruth Oellerman, Christopher Andrew Rodger, and Douglas Robert Stinson. We herewith give summaries of the much more extensive citations and publication lists that were supplied by the nominators of these three scholars.

After obtaining a master's degree at the University of Sydney in Australia, under Jennifer Seberry, Chris Rodger went to the University of Reading for a Ph.D. under the direction of Tony Hilton. He is currently at Auburn University where he holds the position of Alumni Professor in the Department of Discrete and Statistical Science. Author of over seventy papers in a wide diversity of journals, he has made many significant contributions to combinatorics. Among his fundamental results are the proof that a partial idempotent latin square of order n can be embedded in an idempotent latin square of order 2n + 1, as well as a complete solution of the more general problem of embedding a partial latin square with a prescribed diagonal into a (complete) latin square with a prescribed diagonal.

Among other embedding results, Chris has proved that a partial λ-fold triple system of order n can be embedded in a λ -fold triple system of order approximately 4n for all λ. Subsequently, he established the best possible embedding of partial triple systems for all λ ≡ 0 mod 4. All this work involved a constant of new techniques, but his most powerful techniques appeared in his generalization of the embedding and completion theorems due to Hall, Evans, Ryser and Cruse; his results on embedding partial cycle systems reduced the size of the containing cycle system from an exponential order to basically a linear order.

Chris is the leading expert on the spectrum of cycle systems, both directed and undirected, and has obtained fundamental connections between cycle systems and universal algebra. He has also generalized the Doyen-Wilson Theorem to cycle systems other than Steiner triple systems. The techniques he has employed in his papers are innovative and powerful, and his contributions to the theory of embedding designs and the existence of cycle systems are fundamental. He is recognized as the coryphaeus of these areas.