Some results in triply–generated telescopic numerical semigroups
Küçük Resim Yok
Tarih
2017-05
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Harran Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Attribution-NonCommercial-ShareAlike 3.0 United States
Attribution-NonCommercial-ShareAlike 3.0 United States
Özet
In this study, we assume that ¥ = {0,1,2,...,n,...}, S Í ¥ and ¢ integer set.
S is a numerical semigroup if a + b Î S, for a,b Î S , 0Î S and ¥ \S is finite. Let
S be a numerical semigroup and X Ì ¥ . X is called minimal system of generators
of S if S = < X > and there is not any subset Y Ì X such that S = < Y > .
= < > 1 2 3 S s ,s ,s is called a triply-generated telescopic numerical semigroup if
Î < > 1 2
3 ,
s s
s
d d
where = 1 2 d gcd(s s ) (Here, gcd(S)= greatest common divisor the
element of S ). Let S be a numerical semigroup, then m(S) = min{x Î S: x > 0} is
called as multiplicity of S . The number F(S) = max(¢ \S) is called Frobenius
number of S . A numerical semigroup S can be written the form
{ } - = < > = = = + ® 1 2 0 1 2 1 , ,..., 0, , ,..., , ( ) 1, ... n n n S a a a s s s s s F S , where + < i i 1 s s ,
n = n(S) and the arrow means that every integer greater than F(S)+ 1 belongs to S
for i = 1,2,...,n = n(S) .
If x Î ¥ and x Ï S , then x is called gap of S . We denote the set of gaps
ofS , H(S) = ¥ \S . The number G(S) = #(H(S)) is called the genus ofS . Let S be a
numerical semigroup and m Î S ,m> 0. Then Ap(S,m) x S :x mS is
called Apery set of S according to m . Ap(S,m) is formed by the smallest elements
of S belonging to the different congruence classes mod m. Thus # (Ap(S,m)) = m and the Frobenius number of S equal to max(Ap(S,m)) - m ( where #(A) stands for
Cardinality (A) ). The number n(S) = #({0,1,2,...,F(S)}ÇS) is called determine of
numerical semigroup S . Also, It is known that G(S) = F(S)+ 1- n(S) .
In this study, we will give some results about gaps, fundamental gaps and
the determine number of S triply-generated telescopic numerical semigroups with
arbitrary multiplicity.
Açıklama
Anahtar Kelimeler
Frobenius Number, Telescopic Numerical Semigroup, Genus
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Süer, M., İlhan, S. (2017). Some results in triply–generated telescopic numerical semigroups. International Conference on Mathematics and Mathematics Education (ICMME-2017), 11-13 Mayıs 2017, Şanlıurfa
