A short disproof of Euler's conjecture based on quasi-difference matrices and difference matrices

作者：Wang, Kun; Chen, Kejun^*

来源：Discrete Mathematics, 2018, 341(4): 1114-1119.

DOI：10.1016/j.disc.2017.10.019

• Quasi
• Difference matrix
• Orthogonal
• Latin square

In this note, two classes of quasi-difference matrices, (2n + 2, 4; 1, 1; n)-QDM and (4n + 1, 4; 1, 1; 2n 1)-QDM, are constructed. Combining the known results of quasi-difference matrices and difference matrices, a new short disproof of Euler's conjecture on mutually orthogonal Latin squares is given.

• 出版日期2018-4
• 单位南京师范大学; 台州学院