12 sonuçlar
Arama Sonuçları
Listeleniyor 1 - 10 / 12
Öğe On Arf numerical semigroups(SCIK Publishing Corporation, 2016) Süer, Meral; İlhan, SedatIn this study, we obtain an Arf semigroup by means of a sequence. We also establish some results on the Arf semigroupÖğe On telescopic numerical semigroup families with embedding dimension 3(Erzincan Üniversitesi, 2019-03-24) Süer, Meral; İlhan, SedatIn this study, the set of all telescopic numerical semigroups families with embedding dimension three is obtained for some fixed multiplicity by some parameters. Also, some invariants of these families are calculated in term of their generatorsÖğe Katlılığı 6 olan saturated sayısal yarıgruplar üzerine(Batman Üniversitesi, 2017) Süer, Meral; İlhan, Sedat; Çelik, Ahmetİlk olarak sayısal yarıgrup problemi, “ Sayısal yarıgruba ait olmayan en büyük tamsayıyı üreteçleri cinsinden nasıl ifade edilebilir?” şeklinde olup, 19. yy sonunda karşımıza çıkmıştır. Sayısal yarıgrup çalışan ilk matematikçiler Frobenius ve Sylvester’dır. Sayısal yarıgrup kavramı günümüzde de hala matematikçilerin ilgi alanındadır. Sayısal yarıgrup problemleri, sayılar teorisi ile bağlantılı olduğu gibi matematiğin diğer alanlarında ve bilgisayar bilimleri ile de ilgilidir. Diophant moduler eşitsizliklerin çözümünde, liner tamsayı programlamada, şifrelemede, değişmeli cebir ve cebirsel geometrinin uygulamalarında özel ilgi alanı oluşturmuştur. Bu bağlamda saturated sayısal yarıgruplarda literatürde önemli çalışmalarda yer almış. Özellikle saturated halkaların, yarıgruplar teorisine geçişi olarak karşımıza çıkmış. Bu çalışmadaki amacımız katlılığı 6 ve kondüktörü C olan saturated sayısal yarıgruplar üzerine çalışmaktır. Burada C, 6 dan büyük veya eşit ve k negatif olamayan tamsayı olmak üzere 6k+1 den farklı olarak yazılabilen pozitif bir tamsayıdır. Katlılığı 6 ve kondüktörü C olan tüm saturated sayısal yarıgrupları elde edip bu sayısal yarıgrupların Frobenius sayısı, belirteç sayısı ve cinsini bu yarıgrupların üreteçleri ile ifade edeceğiz.Öğe The results on some Arf numerical semigroups with multiplicity 8(İksad Publications, 2019-12-16) Süer, Meral; İlhan, Sedat; Karakaş, İbrahimIn this paper, we will give some results about Frobenius number, Apery set, type, genus and determine number of Arf numerical semigroup S such that m S() 8 = and CS C ( ) 0, 2,3, 4,5,6,7 ( mod8).Öğe On a family of saturated numerical semigroups with multiplicity four(TÜBİTAK, 2017-01-16) Süer, Meral; İlhan, SedatIn this study, we will give some results on Arf numerical semigroups of multiplicity four generated by {4, k, k + 1, k + 2} where k is an integer not less than 5 and k ≡ 1(mod 4).Öğe Saturated numerical semigroups with multiplicity four(Fırat Üniversitesi, 2016-05) Süer, Meral; İlhan, SedatA 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.Öğe İndirgenme boyutu üç olan fibonacci simetrik sayısal yarıgruplarının bir sınıfı(Batman Üniversitesi, 2015) Süer, Meral; İlhan, SedatBu çalışmada, pozitif tam sayı, , ve , 3 ün tam katı olmamak üzere, Fibonacci sayıları için simetrik Fibonacci sayısal yarıgrubu şeklindeki özel bir sınıfını inceleyeceğiz ve bu sınıfta bazı sonuçları vereceğiz.Öğe On the numerical semigroups with generated by two elements with multiplicity 3(Harran Üniversitesi, 2017-05) Süer, Meral; İlhan, Sedat; Çelik, AhmetThroughout this study, we assume that ¥ and ¢ be the sets of nonnegative integers and integers, respectively. The subset S of ¥ is a numerical semigroup if 0 Î S , x + y Î S, for all x, y Î S , and Card(¥ \S)< ¥ ( this condition is equivalent to gcd(S)= 1 , gcd(S)= greatest common divisor the element of S ) . Let S be a numerical semigroup, then F(S) = max(¢ \S) and m(S) = min{s Î S: s > 0} are called Frobenius number and multiplicity of S , respectively. Also, n(S) = Card ({0,1,2,...,F(S)}ÇS)is called the number determine of S . If S is a numerical semigroup such that 1 2 , ,..., r S = < a a a > , then we observe that { } 1 2 0 , 2 1 , ,..., 0, , ,..., , ( ) 1, ... r n n S a a a s s s s s F S - = < > = = = + ® where 1 , ( ) i i 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 a Î ¥ and a Ï S , then a is called gap of S . We denote the set of gaps of S , by H(S) , i.e, H(S) = ¥ \S .The G(S) = Card(H(S)) is called the genus of S . Also, It is known that G(S) = F(S) + 1- n(S) . Let S be a numerical semigroup andm Î S ,m > 0 . Then Ap(S,m) xS :x mS is called Apery set of S according to m . A numerical semigroup S is Arf if a+ b- c Î S , for all a,b,c Î S such that a ³ b ³ c. The intersection of any family of Arf numerical semigroups is again an Arf numerical semigroup. Thus, since ¥ is an Arf numerical semigroup, one can consider the smallest Arf numerical semigroup containing a given numerical semigroup. The smallest Arf numerical semigroup containing a numerical semigroup S is called the Arf closure of S , and it is denoted by Arf (S) . In this presentation, we will give some results about gaps, the determine number, Apery set and Arf closure of S numerical semigroup such that S = 3, x .Öğe On the saturated numerical semigroups(Open Mathematics, 2016-11) Süer, Meral; İlhan, SedatIn this study, we characterize all families of saturated numerical semigroups with multiplicity four. We also present some results about invariants of these semigroups.Öğe On a class of Arf numerical semigroups(Fırat Üniversitesi, 2016-05) Süer, Meral; İlhan, SedatA 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.
