A short disproof of Euler’s conjecture based on quasi-difference matrices and difference matrices. (English) Zbl 1380.05021
Summary: In this note, two classes of quasi-difference matrices, \((2 n + 2, 4; 1, 1; n)\)-QDM and \((4 n + 1, 4; 1, 1; 2 n - 1)\)-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.
MSC:
| 05B20 | Combinatorial aspects of matrices (incidence, Hadamard, etc.) |
| 05B15 | Orthogonal arrays, Latin squares, Room squares |
References:
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