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

Víctor Álvarez ; José Andrés Armario ; María Dolores Frau ; Félix Gudiel

Open Mathematics, Tome 13 (2015), / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2015-01-01

Zbl 1307.05031

EUDML-ID : urn:eudml:doc:268889

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