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A Room Design of Order 14

Published online by Cambridge University Press:  20 November 2018

C D. O'Shaughnessy
C D. O'Shaughnessy*
Affiliation:
University of Windsor
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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 array of side 2n - 1, such that each of the (2n - 1)2 cells of the array is either empty or contains exactly two distinct objects; each of the 2n objects appears exactly once in each row and column; and each (unordered) pair of objects occurs in exactly one cell. A Room design of order 2n is said to be cyclic if the entries in the (i + l) th row are obtained by moving the entries in the i th row one column to the right (with entries in the (2n - l)th column being moved to the first column), and increasing the entries in each occupied cell by l(mod 2n - 1), except that the digit 0 remains unchanged.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 191 - 194
Copyright
Copyright © Canadian Mathematical Society 1968

References

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3. Archbold, J. W., A combinatorial problem of T.G. Room. Mathematika 7 (1960) 50-55.Google Scholar
4. Bruck, R.H., What is a loop? Studies in Modern Algebra. (ed. Albert, A.A., Prentie Hall, 1963).Google Scholar
5. Weisner, L., A Room design of order 10. Canad. Math. Bull. 7 (1964), 377-378.Google Scholar