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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 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 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 Pseudo simetrik sayısal yarıgruplar üzerine(Dicle Üniversitesi, 2013-09) Süer, Meral; İlhan, SedatÖğe Gaps of a class of pseudo symmetric numerical semigroups(Acta Universitatis Apulensis, 2013) Süer, Meral; İlhan, SedatIn this study, we give some results about the gaps, fundamental and special gaps of a pseudo symmetric numerical semigroup in the form of S=< 3, 3+ s, 3+ 2s> for s∈ Z+ and 3 s.Öğe Arf sayısal yarıgrupları(Çankaya Üniversitesi, 2013-06) Süer, Meral; İlhan, SedatÖğe 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 Bazı sayısal yarıgrupların tip dizileri(Erciyes Üniversitesi, 2010-08) Süer, Meral; İlhan, SedatÖğe Some results on Arf numerical semigroups with multiplicity 8(Harran Üniversitesi, 2017-05) Süer, Meral; İlhan, SedatA numerical semigroup is a subset of the set of nonnegative integers (denoted here by ¥ ) closed under addition, containing the zero element and with finite complement in ¥ . Note also that up to isomorphism the set of numerical semigroups classify the set of all submonoids of ( , ) ¥ + . Let S be submonoid of ¥ , the condition of having finite complement in ¥ is equivalent to saying that the greatest common divisor (gcd for short) of its elements is one. Those positive integers which do not belong to S are called gaps of S . The number of gaps of S is called the genus of S and it is denoted by G S( ) . The largest gaps of S is F S( ) if S is different from ¥ . m S s S s ( ) min : 0 = Î > { } are called multiplicity of S , respectively. Also, n S Card F S S ( ) 0,1,2,..., ( ) = Ç ({ } ) is called the number determine of S . If a Î ¥ and a S Ï , 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 known that G S F S n S ( ) ( ) 1 ( ) = + - . A numerical semigroup S is called Arf if x y z S + - Î for all x y z S , , Î , where x y z ³ ³ . This definition was first given by C. Arf in 1949. In the study, we intend to examine the Arf numerical semigroup with multiplicity eight and fixed conductor. We will also able to compute the notable elements and special sets of these numerical semigroups.
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