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Articles 4861 - 4868 of 4868
Full-Text Articles in Physical Sciences and Mathematics
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.
(V, K, Lambda)-Configurations And Hadamard Matrices, Jennifer Seberry
(V, K, Lambda)-Configurations And Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
(v, k, lambda) Configirations and Hadamard matrics
Hadamard Designs, Jennifer Seberry
Hadamard Designs, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
In this paper it is shown that an Hadamard design with each letter repeated once and only once can exist for 2, 4 and 8 letters only. L.D. Baumert and Marshall Hall, Jr have found a design with four letters each repeated three times. Their design and the design on four letters each repeated once, found by J. Williamson, is the totality previously published.
A Note Of A Class Of Hadamard Matrices, Jennifer Seberry
A Note Of A Class Of Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
An Hadamard matrix H is a matrix of order n all of whose elements are + 1 or -1 and which satisfies H ffT = nIn . H = S + In is a skew-type Hadamard matrix if ST = -So It is conjectured that an Hadamard matrix always exists for n = 4t, t any integer. Many known matrices and classes of matrices can be found in [1].
Two New Block Designs, Jennifer Seberry
Two New Block Designs, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
In this note the matrices W, X. Y, and Z are the incidence matrices of the (u, k, ,\,) configurations (15, 7, 3), (25,9,3), (45, 12,3), and (36, 15,6), respectively. Wand X are new formulations of these configurations and Yand Z were previously not known (see [I, pp. 295, 297]).
A Class Of Hadamard Matrices, Jennifer Seberry
A Class Of Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Whenever there exists a quasi-skew Hadamard matrix of order 4m and (4n - I, k, m - n + k) and (4n - I, u, u - n) configurations with circulant incidence matrices, then there exists an Hadamard matrix of order 4m(4n - I).
Equivalence Of Hadamard Matrices, W. D. Wallis, Jennifer Seberry
Equivalence Of Hadamard Matrices, W. D. Wallis, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Suppose In is a square-free odd integer, and A and B are any two Hadamard matrices of order 4m. We will show that A and B are equivalent over the integers (that is, B can be obtained from A using elementary row and column operations which involve only integers).