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arXiv · 2604.25653

On numerical semigroups with embedding dimension four

Kazimierz Chomicz
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Abstract

We develop a geometric procedure for finding the Ap\'ery set of any numerical semigroup with embedding dimension four. Previous methods of comparable strength worked only for embedding dimension three or under very specific conditions. We illustrate our method by finding the Frobenius numbers, genera, Betti elements, minimal presentations, and catenary degrees of numerical semigroups generated by four consecutive squares and by four consecutive triangular numbers.

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Kazimierz Chomicz. 2026-04-28. On numerical semigroups with embedding dimension four. https://arxiv.org/abs/2604.25653

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