Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings

Fuente: arXiv
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Main Authors: Van Kien, Do, Quy, Pham Hung
Format: Preprint
Published: 2026
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_version_ 1866915761215242240
author Van Kien, Do
Quy, Pham Hung
author_facet Van Kien, Do
Quy, Pham Hung
contents Let $a,b$ be positive integers. In this note, we study the numerical semigroup $H=\left<a,a+1,b\right>$ and and the associated numerical semigroup ring $R=k[[H]]$. Under the certain conditions, we provide explicit formulas for the Frobenius number of $H$ and for the first Hilbert coefficient of $R$.
format Preprint
id arxiv_https___arxiv_org_abs_2601_21819
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings
Van Kien, Do
Quy, Pham Hung
Group Theory
Commutative Algebra
Number Theory
20M25, 11D07, 13A15, 13D40
Let $a,b$ be positive integers. In this note, we study the numerical semigroup $H=\left<a,a+1,b\right>$ and and the associated numerical semigroup ring $R=k[[H]]$. Under the certain conditions, we provide explicit formulas for the Frobenius number of $H$ and for the first Hilbert coefficient of $R$.
title Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings
topic Group Theory
Commutative Algebra
Number Theory
20M25, 11D07, 13A15, 13D40
url https://arxiv.org/abs/2601.21819