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On contributions to the theory of near-vector spaces and graphs thereof
Thesis (PhD)--Stellenbosch University, 2020.
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| Other Authors: | |
| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2020
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| _version_ | 1867613784974032896 |
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| access_status_str | Open Access |
| author | Wessels, Lesley Karin |
| author2 | Howell, Karin-Therese |
| author_browse | Howell, Karin-Therese Wessels, Lesley Karin |
| author_facet | Howell, Karin-Therese Wessels, Lesley Karin |
| author_sort | Wessels, Lesley Karin |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2020. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/109139 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:41:39.515Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2020 |
| publishDateRange | 2020 |
| publishDateSort | 2020 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/109139 On contributions to the theory of near-vector spaces and graphs thereof Wessels, Lesley Karin Howell, Karin-Therese Dorfling, Samantha Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics. Finite fields (Algebra) Near-vector spaces Graph theory Vector spaces -- Graphic methods UCTD Thesis (PhD)--Stellenbosch University, 2020. ENGLISH ABSTRACT: In this thesis, our aim is to add to the existing body of work on near-vector spaces and their representation using graphs. We introduce two new graphs for constructions of nearvector spaces using finite fields, the fibration and subspace inclusion graph and study their properties. As a second focus, we look at the quotient spaces of a near-vector space, where some of the maximal regular subspaces have been factored out. For construction of nearvector spaces from copies of finite fields, we completely characterise regularity, describe the quasi-kernel and some of its graphs. We conclude with some reconstruction problems for the near-vector space graphs introduced and one related to finite near-fields. AFRIKAANSE OPSOMMING: In hierdie tesis, beoog ons om by te dra tot die bestaande werke oor naby-vektorruimtes en hul voorstelling met behulp van grafieke. Ons stel twee nuwe grafieke voor, naamlik die fibrasie- en die deelruimte-insluiting grafiek, vir naby-vektorruimters wat van kopieë van eindige liggame gebou is, en bestudeer hul eienskappe. 'n Tweede fokuspunt wat ons beskou is die kwosiëntruimte van 'n naby-vektorruimte, waar ons sekere van die maksimale regulêre deelruimtes uitfaktor. Naby-vektorruimtes wat vanuit kopieë van eindige liggame gebou is, word volledig gekenmerk deur middel van regulêriteit, ons beskryf die kwasiekern sowel as sekere van hul grafieke. Ons sluit af met 'n paar rekonstruksie probleme van naby-vektorruimte grafieke wat voorgestel was, asook een wat verwant is aan eindige naby-liggame. Doctoral 2020-10-23T10:09:17Z 2021-01-31T19:36:49Z 2020-10-23T10:09:17Z 2021-01-31T19:36:49Z 2020-12 Thesis http://hdl.handle.net/10019.1/109139 en_ZA Stellenbosch University viii, 105 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Finite fields (Algebra) Near-vector spaces Graph theory Vector spaces -- Graphic methods UCTD Wessels, Lesley Karin On contributions to the theory of near-vector spaces and graphs thereof |
| title | On contributions to the theory of near-vector spaces and graphs thereof |
| title_full | On contributions to the theory of near-vector spaces and graphs thereof |
| title_fullStr | On contributions to the theory of near-vector spaces and graphs thereof |
| title_full_unstemmed | On contributions to the theory of near-vector spaces and graphs thereof |
| title_short | On contributions to the theory of near-vector spaces and graphs thereof |
| title_sort | on contributions to the theory of near vector spaces and graphs thereof |
| topic | Finite fields (Algebra) Near-vector spaces Graph theory Vector spaces -- Graphic methods UCTD |
| url | http://hdl.handle.net/10019.1/109139 |
| work_keys_str_mv | AT wesselslesleykarin oncontributionstothetheoryofnearvectorspacesandgraphsthereof |