Ralph Gordon Stanton
نویسنده
چکیده
Ralph Stanton was born in Ontario, Canada, on the anniversary of the Battle of Trafalgar, and he died in St Boniface hospital in Winnipeg, at the age of 86. He preferred a simple life, content with a shelf of good books, his stamp collection, a little good food, congenial company, and an interesting problem on which to work. Stanton graduated with a PhD in Mathematics in 1949, and began his teaching career at the University of Toronto. He was one of the earliest staff members appointed in Mathematics at Waterloo, and he also served at York University (Canada) and at the University of Manitoba. During his illustrious, lengthy career he was a Professor, and several times Dean and Department Chairman or Head. Stanton's extremely distinguished academic career spanned 61 years. His distinctions include Killam Laureate, 1985, and honorary doctorates from four universities: D. Stanton commenced his research in group theory, in particular, with the Mathieu groups, in the late forties and early fifties. He then worked on families of difference sets and balanced incomplete block designs (BIBDs), from both combinatorial and statistical points of view. As well as BIBDs, he worked on covering and packing designs, constructions of Room squares, properties of various graphs, and of error-correcting codes. At the time of his death, he was still working on four classes of designs: Doehlert-Klee designs, small projective geometries described in combinato-rial terms, Sarvate-Beam triple systems and butterfly factorizations.
منابع مشابه
On exact bicoverings of 12 points
The minimum number of incomplete blocks required to cover, exactly λ times, all t-element subsets from a set V of cardinality v (v > t) is denoted by g(λ, t; v). The value of g(2, 2; v) is known for v = 3, 4, . . . , 11. It was previously known that 13 ≤ g(2, 2; 12) ≤ 16. We prove that g(2, 2; 12) ≥ 14.
متن کاملA census of minimum pair-coverings with restricted largest block length
The quantity g (k) (v) was introduced in [6] as the minimum number of blocks necessary in a pairwise balanced design on v elements, subject to the condition that the longest block has length k. Recently, we have needed to use all possibilities for such minimal covering designs, and we record all non-isomorphic solutions to the problem for v ≤ 13.
متن کاملMinimal perfect bicoverings of Kv with block sizes two, three and four
This is a preprint of an article accepted for publication in the Ars Combina-toria c 2004 (copyright owner as specified in the journal). Abstract We survey the status of minimal coverings of pairs with block sizes two, three and four when λ = 1, that is, all pairs from a v-set are covered exactly once. Then we provide a complete solution for the case λ = 2.
متن کاملMore on exact bicoverings of 12 points
The minimum number of incomplete blocks required to cover, exactly λ times, all t-element subsets from a set V of cardinality v (v > t) is denoted by g(λ, t; v). The value of g(2, 2; v) is known for v = 3, 4, . . . , 11. It was previously known that 14 ≤ g(2, 2; 12) ≤ 16. We prove that g(2, 2; 12) ≥ 15.
متن کاملStanton Graph Decompositions
Stanton graphs Sk (in honor of professor Ralph G. Stanton) are defined, and a new graph decomposition problem for Stanton graphs is proposed. Such decompositions of λKv for all v’s with minimum λ’s have been obtained for S3.
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 48 شماره
صفحات -
تاریخ انتشار 2010