Decomposition of complete designs
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Date
2019
Authors
Sasani, Sara
University of Lethbridge. Faculty of Arts and Science
Journal Title
Journal ISSN
Volume Title
Publisher
Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science
Abstract
Through six chapters, the concept of decomposing the complete design is demonstrated.
Group divisible designs, symmetric designs, strongly regular graphs, and association schemes
are examples of the combinatorial objects that complete designs are decomposed into.
Reconstructing McFarland designs leads to the existence of sets of designs with disjoint
incidence matrices whose sum is the complete design. The existence of infinite classes of
symmetric association schemes follows from the decomposition.
Applying a similar technique on the Spence designs provides sets of designs all sharing
the same complete tripartite graphs. By appropriately splitting the designs a decomposition
of the complete design is obtained leading to an infinite class of non-commutative association
schemes.
A final attempt is made to combine the constructed decomposition with specific classes
of balanced generalized weighing matrices.
Description
Keywords
Analysis of means , Analysis of variance , Association schemes (Combinatorial analysis) , Decomposition (Mathematics) , Experimental design