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Journals / International Journal of Pure and Applied Sciences / 2024 / Volume: 10 Issue: 2

All Triply Telescopic Numerical Semigroups with Multiplicity 12

Katlılığı 12 Olan Bütün Üçlü Teleskopik Sayısal Yarıgruplar

Ahmet Çelik(ADIYAMAN ÜNİVERSİTESİ)0000-0001-5980-0625
Pages
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Publication Date
2024-12-31
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AI Summary & Key Takeaways

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

We will also give formulas to calculate the genus, determine number and Frobenius number in these semigroups.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Numerical semigroups form a subset of non-negative integers.
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Key Findings & Data:Here we will characterize all telescopic numerical semigroups produced by three elements with multiplicity 12.
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Conclusion & Impact:We will also give formulas to calculate the genus, determine number and Frobenius number in these semigroups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:telescopic numerical semigroup · frobenius · genus

Abstract

Numerical semigroups form a subset of non-negative integers. Of these semigroups, symmetric ones have an important place. It is of particular importance to examine and classify telescopic numerical semigroups, which form a class of symmetric numerical semigroups. Especially finding their Frobenius numbers and spaces is a problem in itself. In this study, we will examine some telescopic numerical semigroups that will contribute to the solution to this problem. Here we will characterize all telescopic numerical semigroups produced by three elements with multiplicity 12. We will also give formulas to calculate the genus, determine number and Frobenius number in these semigroups.

Özet

Sayısal yarıgruplar, negative olmayan tam sayıların bir alt kümesini oluştururlar. Bu sayısal yarıgruplardan simetrik olanlar önemli bir yere sahiptir. Simetrik sayısal yarıgrupların bir sınıfını oluşturan teleskopik sayısal yarıgrupları incelemek ve bun-ları sınıflandırmak ayrı bir önem taşımaktadır. Özellikle bu sayısal yarıgrupların Frobenius sayılarını ve boşluklarını bulmak başlı başına bir problemdir. Bu çalışmada bu probleme çözüm için bir katkı sağlayacak bazı teleskopik sayısal yarıgrupları inceleyeceğiz. Burada, katlılığı 12 olan, üç elemanla üretilen tüm teleskopik sayısal yarıgrupları karakterize edeceğiz. Ayrıca bu yarıgruplarda cins, belirteç sayısı ve Frobenius sayısını hesaplamak için formüller vereceğiz.

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Cite This Article

Çelik, A. (2024). All Triply Telescopic Numerical Semigroups with Multiplicity 12. International Journal of Pure and Applied Sciences, Volume: 10 Issue: 2. https://doi.org/10.29132/ijpas.1579207

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