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On Boolean semiring partitioning
Justus, C. L. 2025. On Boolean semiring partitioning. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/4c2c87b4-e49a-4b02-99cb-171b299e3e27
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| Format: | Thesis |
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Stellenbosch : Stellenbosch University
2025
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| _version_ | 1867613868703875072 |
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| access_status_str | Open Access |
| author | Justus, Claudia Ledbury |
| author2 | Howell, K. T. |
| author_browse | Howell, K. T. Justus, Claudia Ledbury |
| author_facet | Howell, K. T. Justus, Claudia Ledbury |
| author_sort | Justus, Claudia Ledbury |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Justus, C. L. 2025. On Boolean semiring partitioning. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/4c2c87b4-e49a-4b02-99cb-171b299e3e27 |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/132561 |
| institution | Stellenbosch University (South Africa) |
| last_indexed | 2026-06-10T12:42:59.065Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/132561 On Boolean semiring partitioning Justus, Claudia Ledbury Howell, K. T. Hui, Cang Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Algebra, Boolean Semirings (Mathematics) Partitions (Mathematics) UCTD Justus, C. L. 2025. On Boolean semiring partitioning. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/4c2c87b4-e49a-4b02-99cb-171b299e3e27 Thesis (MSc)--Stellenbosch University, 2025. ENGLISH ABSTRACT: In this thesis, our aim is to add to the existing body of work on Q-ideals for semiring partitioning. We introduce a new method for constructing Q-ideals for the partitioning of a class of Boolean commutative semirings. Using this method, we develop a hierarchical partitioning algorithm and prove that it is nested. As a second focus, we prove that initial seeds of equal weight induce equally good Q-ideal partitions, and an initial seed of a lesser weight induces a Q-ideal partition of higher goodness index (than a seed of a greater weight). Finally, we prove that the Q-ideal partition is always a good partition. AFRIKAANSE OPSOMMING: Ons doel met hierdie tesis is om by te dra tot die bestaande werk oor Q-ideale vir die verdeling van halfringe. Ons stel ‘n nuwe metode voor vir die konstruksie van Q-ideale vir die verdeling van ‘n klas van Booleaanse kommutatiewe halfringe. Met behulp van hierdie metode, ontwikkel ons ‘n hi¨erargiese verdelingssalgoritme en bewys dat dit genes is. As ‘n tweede fokus bewys ons dat aanvanklike sade van gelyke gewig ewe goeie Q-ideaalverdelings produseer, en dat ‘n aanvanklike saad van ‘n kleiner gewig ‘n Qideaalverdeling van ‘n ho¨er goedheidsindeks produseer (as ‘n saad van ’n groter gewig). Laastens, bewys ons dat die Q-ideaalverdeling altyd ‘n goeie verdeling is. Masters 2025-06-11T08:03:08Z 2025-06-11T08:03:08Z 2025-03 Thesis https://scholar.sun.ac.za/handle/10019.1/132561 Stellenbosch University vi, 60 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Algebra, Boolean Semirings (Mathematics) Partitions (Mathematics) UCTD Justus, Claudia Ledbury On Boolean semiring partitioning |
| title | On Boolean semiring partitioning |
| title_full | On Boolean semiring partitioning |
| title_fullStr | On Boolean semiring partitioning |
| title_full_unstemmed | On Boolean semiring partitioning |
| title_short | On Boolean semiring partitioning |
| title_sort | on boolean semiring partitioning |
| topic | Algebra, Boolean Semirings (Mathematics) Partitions (Mathematics) UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/132561 |
| work_keys_str_mv | AT justusclaudialedbury onbooleansemiringpartitioning |