On a class of Arf numerical semigroups
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Tarih
2016-05
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Fırat Üniversitesi
Erişim Hakkı
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Özet
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.
Açıklama
Anahtar Kelimeler
Numerical Semigroups, Saturated Numerical Semigroups, Arf Numerical Semigroups, Frobenius Number, Genus, Apery Set
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
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
