Existence of strongly symmetrical weakly pandiagonal graeco-latin squares-Reference-Cited by-同舟云学术

Existence of strongly symmetrical weakly pandiagonal graeco-latin squares

Published:2018-09-01 Issue:1 Volume:6 Page:357-368
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Zhang Yong¹,Chen Kejun²,Li Wen³

Affiliation:

1. School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu, P. R. , China

2. School of Mathematics and Information Science, Nanjing Normal University of Special Education, Nanjing, Jiangsu, P. R. , China

3. School of Science, Xichang University, Sichuan, P. R. , China

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2018-0013/pdf

Reference15 articles.

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