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Duplication of Room squares

Published online by Cambridge University Press:  09 April 2009

W. D. Wallis
W. D. Wallis
Affiliation:
Faculty of Mathematics, University of NewcastleNew South Wales, 2308, Australia
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A Room squareR of order 2n is a way of arranging 2n objects (usually 1,2,…, 2n) in a square array R of side 2n – 1 so that:

(i) every cell of the array is empty or contains two objects;

(ii) each unordered pair of objects occurs once in R

(iii) every row and column of R contains one copy of each object.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 1 , July 1972 , pp. 75 - 81
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Archbold, R. W. and Johnson, N. L., ‘A construction for Room's squares and an application in experimental design’, Ann. Math. Statist. 29 (1958), 219–225.CrossRefGoogle Scholar
[2]Bose, R. C., Parker, E. T. and Shrikhande, S. S., ‘Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler's conjecture’, Canad. J. Math. 12 (1960), 189–203.CrossRefGoogle Scholar
[3]Bruck, R. H., ‘What is a loop?”, Studies in Modern Algebra (ed. Albert, A. A.; Mathematical Association of America, 1963), 59–99.Google Scholar
[4]Mullin, R. C. and Nemeth, E., ‘An existence theorem for Room squares’, Canad. Math. Bull. 12 (1969), 493–497.CrossRefGoogle Scholar
[5]Mullin, R. C. and Nemeth, E., ‘On furnishing Room squares’, J. Combinatorial Theory 7 (1969), 266–272.CrossRefGoogle Scholar
[6]Room, T. G., ‘A new type of magic square’, Math. Gazette 39 (1955), 307.CrossRefGoogle Scholar
[7]Ryser, H. J., Combinatorial Mathematics (Mathematical Association of America, 1963).CrossRefGoogle Scholar
[8]Stanton, R. G. and Mullin, R. C., ‘Construction of Room squares’, Ann. Math. Statist. 39 (1968), 1540–1548.CrossRefGoogle Scholar
[9]Stanton, R. G. and Horton, J. D., Composition of Room Squares, Combinatorial Theory and its Applications (Colloquia Mathematica Societas Janos Bolyai 4) (North Holland, Amsterdam, 1970), 1013–1021.Google Scholar