On a class of Arf numerical semigroups
| dc.authorid | 0000-0002-5512-4305 | en_US |
| dc.contributor.author | Süer, Meral | |
| dc.contributor.author | İlhan, Sedat | |
| dc.date.accessioned | 2021-04-26T09:51:00Z | |
| dc.date.available | 2021-04-26T09:51:00Z | |
| dc.date.issued | 2016-05 | en_US |
| dc.department | Batman Üniversitesi Fen - Edebiyat Fakültesi Matematik Bölümü | en_US |
| dc.description.abstract | A subset S of N is called a numerical semigroup if S is closed under addition and S has element 0 and N\S is finite where N denotes the set of nonnegative integers. In this study, we are interested two subclass of maximal embedding dimension numerical semigroups, which are those semigroups having the Arf property and saturated numerical semigroups. We introduce a new class of both Arf property and saturated numerical semigroups with multiplicity four. We consider numerical semigroups minimally generated by {4, k, k+1, k+2}. Where k is an integer greater than or equal to 5 and k is congruent to 1 (modulo 4). We prove that all these semigroups are both numerical semigroups with Arf property and saturated numerical semigroup. There is not any formulas to calculate invariants as Frobenius number, gaps, n(S) and genus of S even for numerical semigroup with multiplicity four. But this invariants have been calculated by imposing some conditions on elements of the numerical semigroup S. We calculate the Frobenius number, the genus and the set of gaps of each of these numerical semigroups. Additionally, we give a relation between the set of pseudo- Frobenius numbers and the set of all fundamental gaps of these numerical semigroups. | en_US |
| dc.identifier.citation | Süer, M., İlhan, S. (2016). On a class of Arf numerical semigroups. International Conference on Mathematics and Mathematics Education (ICMME-2016), 12-14 Mayıs 2016, Elazığ | en_US |
| dc.identifier.uri | http://theicmme.org/2016/icmme_abstracts_book.aspx | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12402/2991 | |
| dc.language.iso | en | en_US |
| dc.publisher | Fırat Üniversitesi | en_US |
| dc.relation.journal | International Conference on Mathematics and Mathematics Education (ICMME-2016), 12-14 Mayıs 2016 | en_US |
| dc.relation.publicationcategory | Konferans Öğesi - Uluslararası - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Numerical Semigroups | en_US |
| dc.subject | Saturated Numerical Semigroups | en_US |
| dc.subject | Arf Numerical Semigroups | en_US |
| dc.subject | Frobenius Number | en_US |
| dc.subject | Genus | en_US |
| dc.subject | Apery Set | en_US |
| dc.title | On a class of Arf numerical semigroups | en_US |
| dc.type | Conference Object | en_US |
