On Grรถbner Bases via Alternating Semigroup
| dc.contributor.author | Bakare, GN; | |
| dc.contributor.author | Ajibaye, OK; | |
| dc.contributor.author | Usamot, IF; | |
| dc.contributor.author | Ibrahim, GR; | |
| dc.contributor.author | Adeshola, A. D | |
| dc.date.accessioned | 2025-01-29T04:41:34Z | |
| dc.date.available | 2025-01-29T04:41:34Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | Let ฮฉ๐={1, 2,โฆ, ๐} be a finite set ordered in standard way. This paper presents an in-depth investigation into the application of Grรถbner bases within the framework of alternating semigroups (๐ด๐ ๐). The study specifically focuses on the exploration of Grรถbner bases in the context of ๐ด๐ ๐, which forms a subset of the symmetric inverse semigroup (๐ถ๐). Key results derived concerning monomial orderings, including Lexicographic (LEX), Graded Lexicographic (GRLEX), and Graded Reverse Lexicographic (GRVLEX) orders. Monomials are degenerated, and computational techniques employed to achieve the outcomes. The broader significance lies in the potential applications of these results in areas such as combinatorial optimization, symbolic computation, and automated theorem proving. By demonstrating the practical utility of monomial degenerations and computational techniques, this research opens new avenues for efficient problem-solving in both theoretical and applied mathematical domains. A notable observation is that every graded lexicographic ordering of ๐ (๐ด๐ ๐) is a lexicographic order, whereas the converse does not hold. Additionally, ๐ (๐ด๐ ๐) adheres to graded reverse lexicographic order if and only if the index of the first entry of the first monomial is smaller than that of the second monomial. Some classical examples with their graphical representations included to substantiate the theoretical results. | |
| dc.identifier.citation | On Grรถbner Bases via Alternating Semigroup GN Bakare, OK Ajibaye, IF Usamot, GR Ibrahimโฆ - FUOYE Journal of Pure and Applied Sciences (FJPAS), 2024 | |
| dc.identifier.issn | 2616-1419 | |
| dc.identifier.uri | https://kwasuspace.kwasu.edu.ng/handle/123456789/3677 | |
| dc.language.iso | en | |
| dc.publisher | FUOYE Journal of Pure and Applied Sciences (FJPAS) | |
| dc.relation.ispartofseries | FJPAS Vol 9(3) I | |
| dc.title | On Grรถbner Bases via Alternating Semigroup | |
| dc.type | Article |