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arXiv · 2601.21819

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

Do Van Kien·Pham Hung Quy
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Abstract

Let $a,b$ be positive integers. In this note, we study the numerical semigroup $H=\left $ 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 $R$.

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Do Van Kien, Pham Hung Quy. 2026-01-29. Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings. https://arxiv.org/abs/2601.21819

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