Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups

Summary · qwen2.5:32b

The study proves that properties of being nearly Gorenstein or almost symmetric are preserved from $M_n$ to $M_{n+r_k}$ for sufficiently large $n$, by relating their pseudo-Frobenius elements and correcting a previous literature error. Explicit formulas for the Frobenius and pseudo-Frobenius numbers of $M_{n+r_k}$ have also been derived, offering new insights into shifted numerical semigroups' structure.

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Excerpt

arXiv:2601.19629v2 Announce Type: replace Abstract: Given the integers $0<\dots0$. 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 $M_{n+r_k}$.