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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 16 Sayı: 1

On Some Non Perfect Numerical Semigroups With Multiplicity Three

Üçlü Çokluklu Bazı Mükemmel Olmayan Sayısal Yarıgruplar Üzerine

Ahmet Çelik(ADIYAMAN ÜNİVERSİTESİ)0000-0001-5980-0625
Pages
172–182
Publication Date
2026-07-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Our results show that these semigroups are non-perfect, possess the Arf property, and are not symmetric.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we investigate numerical semigroups of multiplicity three of the form Wq= , focusing on their structural properties within the class of maximal embedding dimension (MED) semigroups.
📊
Key Findings & Data:The aim is to determine the position of this class with respect to perfect, Arf, and symmetric numerical semigroups and to describe the behavior of their fundamental invariants.
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Conclusion & Impact:Our results show that these semigroups are non-perfect, possess the Arf property, and are not symmetric.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:maksimal gömme boyutlu sayısal yarı gruplar · izole boşluklar · mükemmel yarı gruplar

Abstract

In this study, we investigate numerical semigroups of multiplicity three of the form Wq= , focusing on their structural properties within the class of maximal embedding dimension (MED) semigroups. The aim is to determine the position of this class with respect to perfect, Arf, and symmetric numerical semigroups and to describe the behavior of their fundamental invariants. Our results show that these semigroups are non-perfect, possess the Arf property, and are not symmetric. Moreover, the Frobenius number, isolated gaps, Apery set, and pseudo-Frobenius numbers exhibit a regular structure within this class. The findings contribute to the structural classification of MED and Arf numerical semigroups and provide potential applications in the study of value semigroups, algebraic curve singularities, and coding theory.

Özet

Bu çalışmada, Wq= biçimindeki üçlü çokluklu (multiplicity three) sayısal yarıgruplar incelenmekte ve bu yarıgrupların maksimal gömme boyutuna (MED) sahip yarıgruplar sınıfı içindeki yapısal özellikleri ele alınmaktadır. Amacımız, bu sınıfın mükemmel, Arf ve simetrik sayısal yarıgruplara göre konumunu belirlemek ve temel değişmezlerinin davranışını açıklamaktır. Elde edilen sonuçlar, bu yarıgrupların mükemmel olmadığını, Arf özelliğini sağladığını ve simetrik olmadığını göstermektedir. Ayrıca, Frobenius sayısı, izole boşluklar, Apéry kümesi ve pseudo-Frobenius sayıları gibi temel değişmezlerin bu sınıf içinde düzenli ve açıkça betimlenebilir bir yapı sergilediği görülmektedir. Bu bulgular, MED ve Arf sayısal yarıgrupların yapısal sınıflandırılmasına katkı sağlamakta olup; değer yarıgrupları, cebirsel eğri tekillikleri ve kodlama teorisi gibi alanlarda potansiyel uygulamalar sunmaktadır.

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Cite This Article

Çelik, A. (2026). On Some Non Perfect Numerical Semigroups With Multiplicity Three. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 16 Sayı: 1, 172–182. https://doi.org/10.37094/adyujsci.1946115

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