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Your search keyword '"Dukes, Peter"' showing total 8 results
Start Over Author "Dukes, Peter" Journal journal of combinatorial designs
8 results on '"Dukes, Peter"'

5. A Three-Factor Product Construction for Mutually Orthogonal Latin Squares.

Author

Dukes, Peter J. and Ling, Alan C.H.

Subjects
*MAGIC squares, *NUMBER theory, *TRANSVERSAL lines, *MATHEMATICS theorems, *MATHEMATICS
Abstract

It is well known that mutually orthogonal latin squares, or MOLS, admit a (Kronecker) product construction. We show that, under mild conditions, 'triple products' of MOLS can result in a gain of one square. In terms of transversal designs, the technique is to use a construction of Rolf Rees twice: once to obtain a coarse resolution of the blocks after one product, and next to reorganize classes and resolve the blocks of the second product. As consequences, we report a few improvements to the MOLS table and obtain a slight strengthening of the famous theorem of MacNeish. [ABSTRACT FROM AUTHOR]

Published
2015
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7. The Asymptotic Existence of Resolvable Group Divisible Designs.

Author

Chan, Justin H., Dukes, Peter J., Lamken, Esther R., and Ling, Alan C.H.

Subjects
*ASYMPTOTIC theory of symmetry groups, *DIVISIBILITY groups, *MATHEMATICAL decomposition, *GRAPH theory, *PARAMETER estimation, *MATHEMATICAL analysis
Abstract

A group divisible design (GDD) is a triple [ABSTRACT FROM AUTHOR]

Published
2013
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