Packings and Coverings of Groups

Dituro, Kyle M.

Student Work

Packings and Coverings of Groups

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Let some finite group G be given. Then a covering of G is a collection of elements C \subseteq G such that for every g \in G, there exists a representation of g as \alpha * beta^{-1}, where alpha, beta \in C. A packing, of G is -- on the other hand -- a collection of elements D a subset of G such that none of the differences in D coincide. Then the primary question associated with these objects involves minimizing the size of a covering, maximizing the size of a packing, and determining when these two definitions meet at a planar difference set. We seek to establish the background of this area of study, provide a comprehensive overview of the current work done regarding these objects, fill in gaps in the current literature, and give a brief introduction to the topics required to approach related problems.

This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

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