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Full-Text Articles in Physical Sciences and Mathematics
The Maximal Determinant And Subdeterminants Of ±1 Matrices, Jennifer Seberry, Tianbing Xia, C. Koukouvinos, M. Mitrouli
The Maximal Determinant And Subdeterminants Of ±1 Matrices, Jennifer Seberry, Tianbing Xia, C. Koukouvinos, M. Mitrouli
Faculty of Informatics - Papers (Archive)
In this paper we study the maximal absolute values of determinants and subdeterminants of ±1 matrices, especially Hadamard matrices. It is conjectured that the determinants of ±1 matrices of order n can have only the values k • p, where p is specified from an appropriate procedure. This conjecture is verified for small values of n. The question of what principal minors can occur in a completely pivoted ±1 matrix is also studied. An algorithm to compute the (n — j) x (n — j), j = 1, 2, ... minors of Hadamard matrices of order n is presented, and …
Short Amicable Sets, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Short Amicable Sets, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Abstract: A pair of matrices X and Y are said to be amicable if XYT = YXT. In this paper, if X and Y are orthogonal designs, group generated or circulant on the group G, these will be denoted 2—SAS(n; ul, u2; G). Recently Kharaghani, in "Arrays for orthogonal designs", J. Combin. Designs, 8 (2000), 166-173, extended this concept to an amicable set, {Ai}2n, i=1, of 2n circulant matrices, which satisfy ∑(Aσ(2i-1)AT σ(2i-1) - Aσ(2i) AT (2i-1) = 0. In this paper we concentrate on constructing short amicable sets, which satisfy the same equation but contain four, called short, or …