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

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Álvarez V., Armario J. A., Frau M. D., Gudiel F.

Open Mathematics

2015

tom 13

nr 1

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.

Ograniczanie wyników

1 Open Mathematics

1 Armario J. A.

1 Frau M. D.

1 Gudiel F.

1 Álvarez V.

1 2015

Wyniki wyszukiwania

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