Imprimitively generated designs
| dc.contributor.author | Lear, Aaron, author | |
| dc.contributor.author | Betten, Anton, advisor | |
| dc.contributor.author | Adams, Henry, committee member | |
| dc.contributor.author | Nielsen, Aaron, committee member | |
| dc.date.accessioned | 2022-08-29T10:16:10Z | |
| dc.date.available | 2022-08-29T10:16:10Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | Designs are a type of combinatorial object which uniformly cover all pairs in a base set V with subsets of V known as blocks. One important class of designs are those generated by a permutation group G acting on V and single initial block b subset of V. The most atomic examples of these designs would be generated by a primitive G. This thesis focuses on the less atomic case where G is imprimitive. Imprimitive permutation groups can be rearranged into a subset of easily understood groups which are derived from G and generate very symmetrical designs. This creates combinatorial restrictions on which group and block combinations can generate a design, turning a question about the existence of combinatorial objects into one more directly involving group theory. Specifically, the existence of imprimitively generated designs turns into a question about the existence of pair orbits of an appropriate size, for smaller permutation groups. This thesis introduces two restrictions on combinations of G and b which can generate designs, and discusses how they could be used to more efficiently enumerate imprimitively generated designs. | |
| dc.format.medium | born digital | |
| dc.format.medium | masters theses | |
| dc.identifier | Lear_colostate_0053N_17363.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/235620 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2020- | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.title | Imprimitively generated designs | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science (M.S.) |
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