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Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach

 

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Opened Access Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach
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Author: Álvarez Solano, Víctor
Armario Sampalo, José Andrés
Frau García, María Dolores
Gudiel Rodríguez, Félix
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2015
Published in: Open Mathematics: Formerly Central European Journal of Mathematics, 13 (1)
Document type: Article
Abstract: An n by n skew-symmetric type (−1, 1)-matrix K = [ki,j ] has 1’s on the main diagonal and ±1’s elsewhere with ki,j = −kj,i. The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n 0 mod 4 (skew- Hadamard matrices), but for n 2 mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (−1, 1)-matrices of skew type. Some explicit calculations have been done up to t = 11. To our knowledge, the upper bounds on the maximal determinant in orders 18 and 22 have been improved.
Cite: Álvarez Solano, V., Armario Sampalo, J.A., Frau García, M.D. y Gudiel Rodríguez, F. (2015). Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach. Open Mathematics: Formerly Central European Journal of Mathematics, 13 (1)
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URI: https://hdl.handle.net/11441/87401

DOI: 10.1515/math-2015-0003

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