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learned many things in the last several years that have helped me in several areas of this thesis. Along with the faculty, I would like to thank the office staff who do much in the department that is unseen, and have certainly done much for me personally. I would also like to thank Phil Romig for teaching me too many things to mention. Also, I would like to… (More)

The existence of group divisible designs of type u'l t with block size three is completely settled for all values of u, r, and t.

- Charles A Cusack
- 1994

1994 This thesis, " PSL(2,q) as an automorphism group of a 3-design with blocksize 5 " , is hereby approved in partial fulfillment for the requirements for the degree of MASTER OF SCIENCE IN MATHEMATICAL SCIENCES, concentration in Discrete Mathematics. Date 2 Acknowledgments I would like to start by thanking the faculty of the Department of Mathematical… (More)

Given a simple, connected graph, a pebbling configuration is a function from its vertex set to the nonnegative integers. A pebbling move between adjacent vertices removes two pebbles from one vertex and adds one pebble to the other. A vertex r is said to be reachable from a configuration if there exists a sequence of pebbling moves that places one pebble on… (More)

- Charles A Cusack
- 2006

I am interested in solving problems related to combinatorial design theory and cryptography by attacking them from two angles—computation and group theory. I am particularly interested in permutation groups—especially PSL(2,q) and closely related groups. The problems I am interested in include establishing the existence of t-designs and large sets, and the… (More)

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