Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
A Skew-Hadamard Matrix Of Order 92, Jennifer Seberry
A Skew-Hadamard Matrix Of Order 92, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Previously the smallest order for which a skew-Hadamard matrix was not known was 92. We construct such a matrix below.
Some (1, -1) Matrices, Jennifer Seberry
Some (1, -1) Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We define an n-type (1, -1) matrix N = 1 + R of order n ~ 2 (mod 4) to have R symmetric and R2 = (n - 1)/n. These matrices are analogous to skewtype matrices M = 1 + W which have W skew-symmetric.
Amicable Hadamard Matrices, Jennifer Seberry
Amicable Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
If X is a symmetric Hadamard matrix, Y is a skew-Hadamard matrix, and XYT is symmetric, then X and Y are said to be amicable Hadamard matrices. A construction for amicable Hadamard matrices is given, and then amicable Hadamard matrices are used to generalize a construction for skew-Hadamard matrices.
Combinatorial Matrices, Jennifer Seberry
Combinatorial Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We investigate the existence of integer matrices B satisfying the equation BBT = rI + sJ where T denotes transpose, r and s are integers, I is the identity matrix and J is the matrix with every element +1.
Some Results On Configurations, Jennifer Seberry
Some Results On Configurations, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
A (v, k, lambda) configuration is conjectured to exist for every v, k and lambda satisfying lambda(v-l) = k(k-l) and k - lambda is a square if v is even, x2 = (k - lambda)y2+(-1)(v-1)/2lamdaZ2 has a solution in integers x,y and z not all zero for v odd.
Integer Matrices Obeying Generalized Incidence Equations, Jennifer Seberry
Integer Matrices Obeying Generalized Incidence Equations, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We consider integer matrices obeying certain generalizations of the incidence equations for (v, k, lambda)-configurations and show that given certain other constraints, a constant multiple of the incidence matrix of a (v, k, lambda)-configuration may be identified as the solution of the equation.