Saturated numerical semigroups with multiplicity four
| dc.authorid | 0000-0002-5512-4305 | en_US |
| dc.contributor.author | Süer, Meral | |
| dc.contributor.author | İlhan, Sedat | |
| dc.date.accessioned | 2021-04-26T09:57:31Z | |
| dc.date.available | 2021-04-26T09:57:31Z | |
| 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. A numerical semigroup S is saturated if the following condition holds: s, s1,s2, …,sk belongs to S are such that s1 < s or equal to s, for all 1 < I < k or i=1 and i=k , and c1,c2,…,ck belongs to are such that c1s1+c2s2+…+cksk > 0 or equal to 0, then s+ c1s1+c2s2+…+cksk belongs to S. The frobenius number of S is the maximum integer not belonging to S, which is denoted by F(S). H(S)= N\S is the set of the elements gaps of S, and the cardinality elements of H(S) is called genus of S, and denoted by g(S). It is said that an integer x is a Pseudo-Frobenius number if x+s belongs to S for s > 0, s belongs to S and x belongs to \S. In this study, we will characterize the all families of Saturated numerical semigroups with multiplicity four. These numerical semigroups generated by 4,k,k 1,k 2 for k>5 or k=5, k=1(mod4), and 4,k,k 2,k 3 for k > 7 or k=7, k=3(mod4), and 4,k,k t,k t 2 for k > 6 or k=6, k=2(mod 4), respectively. We will prove that Saturated numerical semigroups such that multiplicity four. Also, we will give formulas Frobenius number F S( ) , Pseudo Frobenius number PF S( ) , gaps H S( ) and genus g S( ) of these numerical semigroups. | en_US |
| dc.identifier.citation | Süer, M., İlhan, S. (2016). Saturated numerical semigroups with multiplicity four. 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/20.500.12402/2992 | |
| 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 | Saturated Numerical Semigroup | en_US |
| dc.subject | Gaps | en_US |
| dc.subject | Frobenius Number | en_US |
| dc.title | Saturated numerical semigroups with multiplicity four | en_US |
| dc.type | Conference Object | en_US |
