Article
Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach
Author/s | Álvarez Solano, Víctor
Armario Sampalo, José Andrés Frau García, María Dolores Gudiel Rodríguez, Félix |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2015 |
Deposit Date | 2019-06-13 |
Published in |
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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 ... 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. |
Project ID. | FQM-016 |
Citation | 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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