Date of Award

2014

Degree Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Norman J. Finizio

Abstract

In this thesis we introduce a new whist construction which we refer to as The Liaw Variant. This construction is shown to be versatile in that, under appropriate conditions, it can produce every known whist design specialization. No other whist construction in the existing literature can do this. Furthermore, The Liaw Variant is shown to be more powerful than previously published constructions, in that it improves upon the known results related to each of the whist specializations. In particular, under certain applications, we have been able to dramatically reduce previously published asymptotic bounds related to the construction of Z-cyclic directed-triplewhist and ordered-triplewhist designs. This thesis also introduces a new whist specialization, Z-cyclic whist designs that are balanced, directed and ordered but whose initial round partner pairs do not form a patterned starter. We give a new construction capable of producing such designs, and investigate its ability. In some cases, this construction was found to give significant improvements when compared with prior known results. Finally, this thesis introduces a new generalized whist specialization, defining the property of balance on (h; 2h) GWhD(v). A number of existing whist design constructions are shown to either automatically possess the property of balance, or to be modifiable such that balanced designs can be easily obtained. We also show how a modification of another construction will produce balanced (h; 2h) GWhD(v) for certain primes v.

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