Pacific Journal of Mathematics, Volume 2Pacific Journal of Mathematics, 1952 - Electronic journals |
From inside the book
Results 1-3 of 7
Page 335
GROUPS OF ORTHGONAL ROW - LATIN SQUARES DONALD A. NORTON 1. Introduction . An n by n square array of n2 elements , consisting of n dis- tinct elements each repeated n times , will be called a pseudo - latin square . If each row contains ...
GROUPS OF ORTHGONAL ROW - LATIN SQUARES DONALD A. NORTON 1. Introduction . An n by n square array of n2 elements , consisting of n dis- tinct elements each repeated n times , will be called a pseudo - latin square . If each row contains ...
Page 336
latin square . THEOREM 1. The set of all row - latin squares is a group of order ( n ! ) " . Proof . Let be the identity permutation , I - ( 2 ) = Then the square 1 2 • · • 1 2 • · 1 = ( I , J , · 9 J ) = = 1 2 .. • n is the unit ...
latin square . THEOREM 1. The set of all row - latin squares is a group of order ( n ! ) " . Proof . Let be the identity permutation , I - ( 2 ) = Then the square 1 2 • · • 1 2 • · 1 = ( I , J , · 9 J ) = = 1 2 .. • n is the unit ...
Page 337
... row - latin . If they are not or- thogonal , the greco - latin square obtained by composing them contains some re- peated number pair ( u , v ) . Suppose a repeated pair occurs in row m , column p , and in row n ... ROW - LATIN SQUARES 337.
... row - latin . If they are not or- thogonal , the greco - latin square obtained by composing them contains some re- peated number pair ( u , v ) . Suppose a repeated pair occurs in row m , column p , and in row n ... ROW - LATIN SQUARES 337.
Contents
Richard Arens A generalization of normed rings 455 | 11 |
Carlitz Some theorems on Bernoulli numbers of higher order | 127 |
J W S Cassels On a paper of Niven and Zuckerman 555 | 141 |
18 other sections not shown
Other editions - View all
Common terms and phrases
0-cycles A₁ Amer analytic assume b₁ b₂ Boolean bounded C₁ C₂ closed closed sets coefficients compact compact space complete component variety condition conjugate contains continuous continuous functions convergence convex COROLLARY countable cycles defined definition denote disjoint element equation equivalent exists extension factor algebra finite number follows formula function Hausdorff Hausdorff space Hence homomorphism hypothesis ideal implies inequality integral intersection irreducible latin squares Lemma linear locally compact mapping Math maximal metric space necessary and sufficient nontrivial obtain open sets operator orthogonal P₁ polynomial proof of Theorem properties prove pseudo-metric quadric quasi-convex respectively result Riemannian manifold row-latin squares satisfies semigroup sequence subalgebra subset Suppose Theorem topology transformation UNIVERSITY OF CALIFORNIA v₁ vector zero Σ Σ