Packings and Coverings of Groups
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open in viewerLet 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.
- Creator
- Subject
- Publisher
- Identifier
- 22556
- E-project-050521-215924
- Keyword
- Advisor
- Year
- 2021
- Date created
- 2021-05-05
- Resource type
- Major
- Rights statement
- License
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Thumbnail | Title | Visibility | Embargo Release Date | Actions |
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Dituro_MQP_Pack_Cov.pdf | Public | Download |
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