On the Construction of Sets of Orthogonal Latin Squares
نویسندگان
چکیده
منابع مشابه
Maximal sets of mutually orthogonal Latin squares
Maximal sets of s mutually orthogonal Latin squares of order v are constructed for in nitely many new pairs (s; v). c © 1999 Published by Elsevier Science B.V. All rights reserved
متن کاملComplete Sets of Orthogonal Self-Orthogonal Latin Squares
We show how to produce algebraically a complete orthogonal set of Latin squares from a left quasifield and how to generate algebraically a maximal set of self-orthogonal Latin squares from a left nearfield. For a left Veblen-Wedderburn system, we establish the algebraic relationships between the standard projective plane construction of a complete set of Latin squares, our projective plane cons...
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چکیده ندارد.
15 صفحه اولOn the Construction of Sets of Mutually Orthogonal Latin Squares and the Falsity of a Conjecture of Eulero)
then it is known, MacNeish [16] and Mann [17] that there exists a set of at least n(v) mutually orthogonal Latin squares (m.o.l.s.) of order v. It seemed plausible that n(v) is also the maximum possible number of m.o.l.s. of order v. This would have implied the correctness of Euler's [13] conjecture about the nonexistence of two orthogonal Latin squares of order v when v = 2 (mod 4), since n(v)...
متن کاملNearly Orthogonal Latin Squares
A Latin square of order n is an n by n array in which every row and column is a permutation of a set N of n elements. Let L = [li,j ] and M = [mi,j ] be two Latin squares of even order n, based on the same N -set. Define the superposition of L onto M to be the n by n array A = (li,j ,mi,j). When n is even, L and M are said to be nearly orthogonal if the superposition of L onto M has every order...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1943
ISSN: 0003-4851
DOI: 10.1214/aoms/1177731360