Existence of strongly symmetrical weakly pandiagonal graeco-latin squares

Abstract

A graeco-latin sauare is a pair of orthogonal latin squares. It is a design of experiment in which the experimental units are grouped in three different ways. In this paper, constructions of a pair of orthogonal latin sauares which are both strongly symmetrical and weakly pandiagonal are investigated. As a result, it is proved that there exists a pair of strongly symmetrical weakly pandiagonal orthogonal latin sauare of order n if and only if n > 4 and n ≡ 0, 1, 3 (mod 4) with only one possible exception for n = 12.

Keywords

• latin square
• graeco
• orthogonal
• strongly symmetrical
• weakly pandiagonal