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Medientyp:
E-Artikel
Titel:
ON THE EXISTENCE OF ORTHOGONAL LATIN SQUARES WITH SYMMETRIC STRUCTURAL PROPERTY
Beteiligte:
PONNUSWAMY, K. N.;
SUBBARAYAN, A.;
MUKHOPADHYAY, A. C.
Erschienen:
INDIAN STATISTICAL INSTITUTE, 1992
Erschienen in:
Sankhyā: The Indian Journal of Statistics, Series B (1960-2002), 54 (1992), Seite 311-314
Sprache:
Englisch
ISSN:
0581-5738
Entstehung:
Anmerkungen:
Beschreibung:
The solution to the problem concerning the existence and number of mutually orthogonal latin squares with left diagonal elements in natural order has been pretty well known in the literature. In this paper, we address a new problem, where we impose conditions on the elements of the latin square in addition to the condition on the left diagonal being in natural order so that eij = k, then ejk and eki should be i and j respectively for all i ≠ j, where eij denotes the element of the latin square in the cell (i, j). Do such types of latin squares always exist? Do there exist mutually orthogonal latin squares with the stated property? In the present investigation, an attempt has been made to solve these problems partially when n is a prime or a prime-power. Latin squares with the stated property and orthogonal latin squares of the type are found to be extremely useful in the construction of partial triallel mating designs used in connection with the estimation of genetic components of variance (Subbarayan (1988) and Ponnuswamy and Subbarayan (1987)).