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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
In this paper we give formulas, in terms of a, b, c, d, for the genus, the Frobenius number, and the set of pseudo-Frobenius numbers of ⟨a, b, cb − da⟩ in the case in which the interval $[a/c, b/d]$ contains some integer.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:If S is a numerical semigroup with embedding dimension equal to three whose minimal generators are pairwise relatively prime numbers, then S = ⟨a, b, cb − da⟩ with a, b, c, d positive integers such that gcd(a, b) = gcd(a,c) = gcd(b,d) = 1, c ∈ {2,...,a−1}, and a < b < cb−da.
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Temel Bulgular & Veri:If S is a numerical semigroup with embedding dimension equal to three whose minimal generators are pairwise relatively prime numbers, then S = ⟨a, b, cb − da⟩ with a, b, c, d positive integers such that gcd(a, b) = gcd(a,c) = gcd(b,d) = 1, c ∈ {2,...,a−1}, and a < b < cb−da.
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Sonuç & Katkı:In this paper we give formulas, in terms of a, b, c, d, for the genus, the Frobenius number, and the set of pseudo-Frobenius numbers of ⟨a, b, cb − da⟩ in the case in which the interval $[a/c, b/d]$ contains some integer.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Frobenius problem · numerical semigroups · Apéry set
Abstract
If S is a numerical semigroup with embedding dimension equal to three whose minimal generators are pairwise relatively prime numbers, then S = ⟨a, b, cb − da⟩ with a, b, c, d positive integers such that gcd(a, b) = gcd(a,c) = gcd(b,d) = 1, c ∈ {2,...,a−1}, and a < b < cb−da. In this paper we give formulas, in terms of a, b, c, d, for the genus, the Frobenius number, and the set of pseudo-Frobenius numbers of ⟨a, b, cb − da⟩ in the case in which the interval $[a/c, b/d]$ contains some integer.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
ROBLES-PÉREZ, A. M., ROSALES, J. C. (2022). The frobenius problem for some numerical semigroups with embedding dimension equal to three. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 4, 901–908. https://ajindex.com/articles/530260