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Orthomorphisms of Groups and Orthogonal Latin Squares. I

Published online by Cambridge University Press:  20 November 2018

Diane M. Johnson ,
A. L. Dulmage  and
N. S. Mendelsohn
Diane M. Johnson
Affiliation:
University of Manitoba
A. L. Dulmage
Affiliation:
University of Manitoba
N. S. Mendelsohn
Affiliation:
University of Manitoba
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Euler (6) in 1782 first studied orthogonal latin squares. He showed the existence of a pair of orthogonal latin squares for all odd n and conjectured their non-existence for n = 2(2k + 1). MacNeish (8) in 1921 gave a construction of n — 1 mutually orthogonal latin squares for n = p with p prime and of n(v) mutually orthogonal squares of order v where

with p1 p2, … , Pr being distinct primes and

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 356 - 372
Copyright
Copyright © Canadian Mathematical Society 1961

References

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