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arXiv · 2506.11554

Numerical semigroups from rational matrices III: semigroups of matricial dimension two and a counterexample to the lonely element conjecture

Arsh Chhabra·Stephan Ramon Garcia
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Abstract

We characterize semigroups in $\{0,1,2,\ldots\}$ of matricial dimension $2$ and produce a counterexample to the conjecture that a numerical semigroup whose small elements are lonely has matricial dimension at most $2$.

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Arsh Chhabra, Stephan Ramon Garcia. 2025-06-13. Numerical semigroups from rational matrices III: semigroups of matricial dimension two and a counterexample to the lonely element conjecture. https://arxiv.org/abs/2506.11554

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