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An Existence Theorem for Room Squares*

Published online by Cambridge University Press:  20 November 2018

R. C. Mullin  and
E. Nemeth
R. C. Mullin
Affiliation:
University of Waterloo Waterloo, Ontario
E. Nemeth
Affiliation:
Florida Atlantic University-Boca Raton, Florida 33432 497
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It is shown that if v is an odd prime power, other than a prime of the form 22n + 1, then there exists a Room square of order v + 1.

A room square of order 2n, where n is a positive integer, is an arrangement of 2n objects in a square array of 2 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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 493 - 497
Copyright
Copyright © Canadian Mathematical Society 1969

Footnotes

*

Work supported in part by NRC Grant No. A-3071

References

1. Archbold, J. W. and Johnson, N. L., A Construction for Room's squares and an application in experimental design. Ann. Math. Stat. 29 (1958) 219–225.Google Scholar
2. Mullin, R. C. and Nemeth, E., On furnishing Room squares, (to appear)Google Scholar
3. Stanton, R. G. and Mullin, R. C., Construction of Room squares. Ann. Math. Stat. 39 (1968) 1540–1548.Google Scholar
4. Stanton, R. G., A multiplication theorem for Room squares, (to appear)Google Scholar