Acta Mathematica Sinica, English Series

, Volume 29, Issue 6, pp 1089–1094

Existence of weakly pandiagonal orthogonal Latin squares

Article

DOI: 10.1007/s10114-013-2274-1

Cite this article as:
Zhang, Y., Li, W. & Lei, J.G. Acta. Math. Sin.-English Ser. (2013) 29: 1089. doi:10.1007/s10114-013-2274-1

Abstract

A weakly pandiagonal Latin square of order n over the number set {0, 1, ..., n − 1} is a Latin square having the property that the sum of the n numbers in each of 2n diagonals is the same. In this paper, we shall prove that a pair of orthogonal weakly pandiagonal Latin squares of order n exists if and only if n ≡ 0, 1,3 (mod 4) and n ≠ 3.

Keywords

Latin square weakly pandiagonal Knut Vik design 

MR(2010) Subject Classification

05B15 

Supplementary material

10114_2013_2274_MOESM1_ESM.tex (19 kb)
Supplementary material, approximately 19.4 KB.

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuangP. R. China