Charles A. Cusack

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Let 5f be a finite set of x elements, and let G = { G1, G2, ..., Gs} be a par t i t ion of ~r into subsets cal led groups. Let N be a col lect ion of subsets of X cal led blocks, and let set i f = {[B] : B s N ' } , be the set of block sizes. If (~r, N ) has the p r o p e r t y tha t every pa i r of e lements ei ther appears in exact ly one b lock or in(More)
Consider a connected graph and a configuration of pebbles on its vertices. A pebbling step consists of removing two pebbles from a vertex and placing one on an adjacent vertex. A configuration is called solvable if it is possible to place a pebble on any given vertex through a sequence of pebbling steps. A smallest number t such that any configuration with(More)
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)
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)
53 Music theorists face many challenges when analyzing music written according to George Perle’s compositional theory of twelve-tone tonality, a system based on inversional symmetry. Analysts focusing on Mr. Perle’s music seek relationships among collections of notes in an effort to discover connections within and across a specific work. It is often(More)
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