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June, 1952 A Generalization of a Theorem due to MacNeish
K. A. Bush
Ann. Math. Statist. 23(2): 293-295 (June, 1952). DOI: 10.1214/aoms/1177729449


In 1922 MacNeish [1] considered the problem of orthogonal Latin squares and showed that if the number $s$ is written in standard form: $s = p^{n_0}_0p^{n_1}_1 \cdots p^{n_k}_k,$ where $p_0, p_1, \cdots, p_k$ are primes, and if $r = \min(p^{n_0}_0, p^{n_1}_1, \cdots, p^{n_k}_k),$ then we can construct $r - 1$ orthogonal Latin squares of side $s$. An alternative proof was also given by Mann [2]. At the April, 1950 meeting of the Institute of Mathematical Statistics at Chapel Hill, North Carolina, R. C. Bose announced an interesting generalization of this result [3] which is stated as a theorem in the next section. The proof given here is simpler than Bose's original proof and is published at his suggestion.


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K. A. Bush. "A Generalization of a Theorem due to MacNeish." Ann. Math. Statist. 23 (2) 293 - 295, June, 1952.


Published: June, 1952
First available in Project Euclid: 28 April 2007

zbMATH: 0047.01702
MathSciNet: MR49145
Digital Object Identifier: 10.1214/aoms/1177729449

Rights: Copyright © 1952 Institute of Mathematical Statistics

Vol.23 • No. 2 • June, 1952
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