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PreprintarXiv licencearXiv

A criterion for determinantal presentations of numerical semigroup rings

  • Satoshi Murai
  • Kou Takahashi
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Abstract

We study numerical semigroups whose defining ideals admit determinantal presentations by the 2×2 minors of a 2× n matrix. A conjecture of Cuong, Kien, Matsuoka, and Truong relates such presentations to arithmetic progressions of pseudo-Frobenius numbers. We prove a numerical criterion for this determinantal presentation, reducing the conjecture to a problem on factorizations of maximal elements of an Apéry set in the numerical semigroup. As an application, we verify the conjecture in embedding dimension four under a unique factorization assumption on an Apéry set.

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Cite

BibTeXRIS
BibTeX
@misc{murai2026criterion,
  title = {{A criterion for determinantal presentations of numerical semigroup rings}},
  author = {Satoshi Murai and Kou Takahashi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18136},
  eprint = {2609.18136},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18136},
}
RIS
TY  - UNPB
TI  - A criterion for determinantal presentations of numerical semigroup rings
AU  - Satoshi Murai
AU  - Kou Takahashi
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18136
UR  - https://arxiv.org/abs/2609.18136
AB  - We study numerical semigroups whose defining ideals admit determinantal presentations by the 2×2 minors of a 2× n matrix. A conjecture of Cuong, Kien, Matsuoka, and Truong relates such presentations to arithmetic progressions of pseudo-Frobenius numbers. We prove a numerical criterion for this determinantal presentation, reducing the conjecture to a problem on factorizations of maximal elements of an Apéry set in the numerical semigroup. As an application, we verify the conjecture in embedding dimension four under a unique factorization assumption on an Apéry set.
ER  -