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Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecture

Published online by Cambridge University Press:  20 November 2018

R. C. Bose ,
S. S. Shrikhande  and
E. T. Parker
R. C. Bose
Affiliation:
University of North Carolina, Case Institute of Technology and Remington Rand Univac, St. Paul, Minnesota
S. S. Shrikhande
Affiliation:
University of North Carolina, Case Institute of Technology and Remington Rand Univac, St. Paul, Minnesota
E. T. Parker
Affiliation:
University of North Carolina, Case Institute of Technology and Remington Rand Univac, St. Paul, Minnesota
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If

is the prime power decomposition of an integer v, and we define the arithmetic function n(v) by

then it is known, MacNeish (10) and Mann (11), that there exists a set of at least n(v) mutually orthogonal Latin squares (m.o.l.s.) of order v. We shall denote by N(v) the maximum possible number of mutually orthogonal Latin squares of order v. Then the Mann-MacNeish theorem can be stated as

MacNeish conjectured that the actual value of N(v) is n(v).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 189 - 203
Copyright
Copyright © Canadian Mathematical Society 1960

References

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