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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

A VARIATION ON MUTUALLY ORTHOGONAL LATIN SQUARES

Gunawardana, Beruwalage Lakshika Kumari 01 August 2016 (has links)
A Latin square of order n is an n × n array in which each row and column contains symbols from an n-set, S = {a1,...,an}, exactly once. If two Latin squares L1 and L2 of the same order can be joined such that each of the n^2 ordered pairs (ai,aj) appears exactly once, then L1 and L2 are said to be orthogonal. This project will involve a variation of this idea. We define orthogonality of two Latin squares Lm and Ln, for m < n, as follows: When we place an m × m Latin square Lm inside an n × n Latin square Ln, in all possible ways, the so obtained m^2 ordered pairs (ai,aj) are always distinct. We first investigate the situation when m = 2 and n = p, where p is a prime.

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