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arXiv · 2601.19629

Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups

Dumitru I. Stamate·Francesco Strazzanti
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Abstract

Given the integers $0 0$. For sufficiently large $n$, we prove that if $M_n$ is nearly Gorenstein or almost symmetric, then so is $M_{n+r_k}$. A key ingredient is to relate the pseudo-Frobenius elements of $M_n$ and $M_{n+r_k}$, correcting a wrong claim in the literature. Moreover, we derive explicit formulas for the Frobenius and pseudo-Frobenius numbers of $M_{n+r_k}$.

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Dumitru I. Stamate, Francesco Strazzanti. 2026-01-27. Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups. https://doi.org/10.1016/j.jpaa.2026.108330

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