Saturated numerical semigroups with multiplicity four
Küçük Resim Yok
Tarih
2016-05
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Fırat Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/closedAccess
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. 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.
Açıklama
Anahtar Kelimeler
Saturated Numerical Semigroup, Gaps, Frobenius Number
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
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
