Existence of weakly pandiagonal orthogonal Latin squares

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.

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Correspondence to Yong Zhang.

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Supported by National Natural Science Foundation of China (Grant Nos. 61071221, 10831002, 11071207 and 11201407), Natural Science Foundation of Jiangsu Higher Education Institutions of China (Grant No. 12KJD110007), and Natural Science Foundation of Jiangsu Province (Grant No. BK2012245)

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Zhang, Y., Li, W. & Lei, J.G. Existence of weakly pandiagonal orthogonal Latin squares. Acta. Math. Sin.-English Ser. 29, 1089–1094 (2013). https://doi.org/10.1007/s10114-013-2274-1

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Keywords

  • Latin square
  • weakly pandiagonal
  • Knut Vik design

MR(2010) Subject Classification

  • 05B15