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A Room Design of Order 10

Published online by Cambridge University Press:  20 November 2018

Louis Weisner
Louis Weisner*
Affiliation:
University of New Brunswick
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A Room design of order 2n, where n is a positive integer, is an arrangement of 2n objects in a square of side 2n - 1, so that each of the (2n - 1)2 cells of the array is either empty or contains just two distinct objects; each of the 2n objects occurs just once in each row and in each column; and each (unordered) pair of objects occurs in just one cell.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 3 , September 1964 , pp. 377 - 378
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Archbold, J. W., A Combinatorial Problem of T. G. Room, Mathematika 7, 50–55 (1960).Google Scholar
2. Archbold, J. W. and Johnson, N. L., A Construction for Room's Squares and an Application in Experimental Design, Annals of Mathematical Statistics 29, 219–225 (1959).Google Scholar
3. Bruck, R. H., What is a Loop? Studies in Modern Algebra, A. A. Albert (editor), Prentice-Hall (1963).Google Scholar
4. Room, T. G., A New Type of Magic Square, Mathematical Gazette 39, 307 (1955).Google Scholar