Abstract
Skew Hadamard matrices of order n give the solution to the question of finding the largest possible n by n determinant with entries ± 1 of skew type when \(n \equiv 0\pmod 4\). Characterizations of skew Hadamard matrices in terms of tournaments are well-known. For \(n \equiv 2\pmod 4\), we give a characterization of (−1, 1)-matrices of skew type of order n where their determinants reach Ehlich–Wojtas’ bound in terms of tournaments.
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References
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Acknowledgements
The author would like to thank the anonymous referee for his valuable comments. The author would also like to thank Kristeen Cheng for her reading of this manuscript. This work has been partially supported by the research project FQM-016 from JJAA (Spain).
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Dedicated to Hadi Kharaghani on the occasion on his 70th birthday
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Armario, J.A. (2015). On (−1, 1)-Matrices of Skew Type with the Maximal Determinant and Tournaments. In: Colbourn, C. (eds) Algebraic Design Theory and Hadamard Matrices. Springer Proceedings in Mathematics & Statistics, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-319-17729-8_1
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DOI: https://doi.org/10.1007/978-3-319-17729-8_1
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