Bu calismada, pozitif tam sayi, , ve , 3 un tam kati olmamak uzere, Fibonacci sayilari icin simet... more Bu calismada, pozitif tam sayi, , ve , 3 un tam kati olmamak uzere, Fibonacci sayilari icin simetrik Fibonacci sayisal yarigrubu seklindeki ozel bir sinifini inceleyecegiz ve bu sinifta bazi sonuclari verecegiz.
Acta Universitatis Apulensis. Mathematics - Informatics, 2009
In this study, we give some results on pseudo-symmetric numerical semigroups which generated by t... more In this study, we give some results on pseudo-symmetric numerical semigroups which generated by three elements, and we investigate the sutructures S d and I d , for d a positive integer and I an ideal of S pseudosymmetric numerical semigroup.
The aim of this work is to exhibit the relationship between the Arf closure of a numerical semigr... more The aim of this work is to exhibit the relationship between the Arf closure of a numerical semigroup S and its Lipman semigroup L(S). This relationship is then used to give direct proofs of some characterizations of Arf numerical semigroups through their Lipman sequences of semigroups. We also give an algorithmic construction of the Arf closure of a numerical semigroup via its Lipman sequence of semigroups.
Journal of semigroup theory and applications, Oct 28, 2015
In this study, we will characterize the Arf numerical semigroup that is computed in a quotient of... more In this study, we will characterize the Arf numerical semigroup that is computed in a quotient of an Arf numerical semigroup by an positive integer. We will also obtain the one half of this special Arf numerical semigroup and give some results about this numerical semigroup.
Erzincan University Journal of Science and Technology, Mar 24, 2019
In this study, the set of all telescopic numerical semigroups families with embedding dimension t... more In 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 generators.
Bitlis Eren üniversitesi fen bilimleri dergisi, Mar 24, 2022
Let be a numerical semigroup. The catenary degree of an element in is a nonnegative integer used ... more Let be a numerical semigroup. The catenary degree of an element in is a nonnegative integer used to measure the distance between factorizations of. The catenary degree of the numerical semigroup is obtained at the maximum catenary degree of its elements. The maximum catenary degree of is attained via Betti elements of with complex properties. The Betti elements of can be obtained from all minimal presentations of. A presentation for is a system of generators of the kernel congruence of the special factorization homomorphism. A presentation is minimal if it can not be converted to another presentation, that is, any of its proper subsets is no longer a presentation. The Delta set of is a factorization invariant measuring the complexity of sets of the factorization lengths for the elements in. In this study, we will mainly express the given above invariants of a special pseudosymmetric numerical semigroup family in terms of its generators.
Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work,... more Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work, we give parametrizations of Arf numerical semigroups with multiplicity 11 and 13 , and combining these results with previous results about the number of Arf numerical semigroups with multiplicity 2, 3, 5, 7 , we share some observations about the set of Arf numerical semigroups with prime multiplicity.
In this paper, we investigate the row-factorization matrices of Arf numerical semigroups, and we ... more In this paper, we investigate the row-factorization matrices of Arf numerical semigroups, and we provide the full list of such matrices of certain Arf numerical semigroups. We use the information of row-factorization matrices to detect the generic nature and to find generators of the defining ideals.
In this paper, we introduce the concept of Arf special gaps of an Arf numerical semigroup, and an... more In this paper, we introduce the concept of Arf special gaps of an Arf numerical semigroup, and an algorithm for computing all Arf special gaps of a given Arf numerical semigroup. We introduce the concept of Arf-irreducible numerical semigroups, and draw conclusions about all these concepts. We give a system of generators for the Frobenius variety and variety of families of Arf numerical semigroups. Moreover, we obtain the minimal Arf system of generators of a given Arf numerical semigroup.
Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work,... more Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work, we give parametrizations of Arf numerical semigroups with multiplicity 11 and 13 , and combining these results with previous results about the number of Arf numerical semigroups with multiplicity 2, 3, 5, 7 , we share some observations about the set of Arf numerical semigroups with prime multiplicity.
Bu calismada, pozitif tam sayi, , ve , 3 un tam kati olmamak uzere, Fibonacci sayilari icin simet... more Bu calismada, pozitif tam sayi, , ve , 3 un tam kati olmamak uzere, Fibonacci sayilari icin simetrik Fibonacci sayisal yarigrubu seklindeki ozel bir sinifini inceleyecegiz ve bu sinifta bazi sonuclari verecegiz.
Acta Universitatis Apulensis. Mathematics - Informatics, 2009
In this study, we give some results on pseudo-symmetric numerical semigroups which generated by t... more In this study, we give some results on pseudo-symmetric numerical semigroups which generated by three elements, and we investigate the sutructures S d and I d , for d a positive integer and I an ideal of S pseudosymmetric numerical semigroup.
The aim of this work is to exhibit the relationship between the Arf closure of a numerical semigr... more The aim of this work is to exhibit the relationship between the Arf closure of a numerical semigroup S and its Lipman semigroup L(S). This relationship is then used to give direct proofs of some characterizations of Arf numerical semigroups through their Lipman sequences of semigroups. We also give an algorithmic construction of the Arf closure of a numerical semigroup via its Lipman sequence of semigroups.
Journal of semigroup theory and applications, Oct 28, 2015
In this study, we will characterize the Arf numerical semigroup that is computed in a quotient of... more In this study, we will characterize the Arf numerical semigroup that is computed in a quotient of an Arf numerical semigroup by an positive integer. We will also obtain the one half of this special Arf numerical semigroup and give some results about this numerical semigroup.
Erzincan University Journal of Science and Technology, Mar 24, 2019
In this study, the set of all telescopic numerical semigroups families with embedding dimension t... more In 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 generators.
Bitlis Eren üniversitesi fen bilimleri dergisi, Mar 24, 2022
Let be a numerical semigroup. The catenary degree of an element in is a nonnegative integer used ... more Let be a numerical semigroup. The catenary degree of an element in is a nonnegative integer used to measure the distance between factorizations of. The catenary degree of the numerical semigroup is obtained at the maximum catenary degree of its elements. The maximum catenary degree of is attained via Betti elements of with complex properties. The Betti elements of can be obtained from all minimal presentations of. A presentation for is a system of generators of the kernel congruence of the special factorization homomorphism. A presentation is minimal if it can not be converted to another presentation, that is, any of its proper subsets is no longer a presentation. The Delta set of is a factorization invariant measuring the complexity of sets of the factorization lengths for the elements in. In this study, we will mainly express the given above invariants of a special pseudosymmetric numerical semigroup family in terms of its generators.
Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work,... more Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work, we give parametrizations of Arf numerical semigroups with multiplicity 11 and 13 , and combining these results with previous results about the number of Arf numerical semigroups with multiplicity 2, 3, 5, 7 , we share some observations about the set of Arf numerical semigroups with prime multiplicity.
In this paper, we investigate the row-factorization matrices of Arf numerical semigroups, and we ... more In this paper, we investigate the row-factorization matrices of Arf numerical semigroups, and we provide the full list of such matrices of certain Arf numerical semigroups. We use the information of row-factorization matrices to detect the generic nature and to find generators of the defining ideals.
In this paper, we introduce the concept of Arf special gaps of an Arf numerical semigroup, and an... more In this paper, we introduce the concept of Arf special gaps of an Arf numerical semigroup, and an algorithm for computing all Arf special gaps of a given Arf numerical semigroup. We introduce the concept of Arf-irreducible numerical semigroups, and draw conclusions about all these concepts. We give a system of generators for the Frobenius variety and variety of families of Arf numerical semigroups. Moreover, we obtain the minimal Arf system of generators of a given Arf numerical semigroup.
Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work,... more Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work, we give parametrizations of Arf numerical semigroups with multiplicity 11 and 13 , and combining these results with previous results about the number of Arf numerical semigroups with multiplicity 2, 3, 5, 7 , we share some observations about the set of Arf numerical semigroups with prime multiplicity.
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