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Öğe On the fundamental gaps of some saturated numerical semigroups with multiplicity 4(Hikari, 2016) Süer, Meral; İlhan, Sedat; Çelik, AhmetIn this study, we calculate the number of fundamental gaps of the some numerical semigroups which are for and and for and and or. Also, we give the type sequence of these numerical semigroups.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 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.
