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A Partial Generalization of Mann's Theorem Concerning Orthogonal Latin Squares

Published online by Cambridge University Press:  20 November 2018

E. T. Parker  and
Lawrence Somer
E. T. Parker
Affiliation:
Mathematics Department, University of Illinois1409 W. Green Street, Urbana, Illinois 61801
Lawrence Somer
Affiliation:
Mathematics Department, Catholic University of America, Washington, D.C.20064
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Abstract

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Let n = 4t +- 2, where the integer t ≧ 2. A necessary condition is given for a particular Latin square L of order n to have a complete set of n — 2 mutually orthogonal Latin squares, each orthogonal to L. This condition extends constraints due to Mann concerning the existence of a Latin square orthogonal to a given Latin square.

Keywords

05B15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 409 - 413
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Hall, M., Combinatorial Theory Blaisdell Publishing Company, Waltham, Massachusetts, 1967.Google Scholar
2. Mann, Henry B., On orthogonal latin squares Bull. Amer. Math. Soc, Vol. 50, 1944, pp. 249–257.Google Scholar
3. Ryser, H. J., Combinatorial Mathematics Mathematical Association of America, Washington, D.C., 1963.Google Scholar
4. Woodcock, C. F., On orthogonal latin squares J. Combin. Theory Ser. A., Vol. 43, 1986, pp. 146–148.Google Scholar