Pré-Publication, Document De Travail Année : 2025

Numerical semigroup tree: type-representation

Résumé

In this paper, we introduce a new depicting of the so-called numerical semigroup tree $\mathcal T$. By exploring computationally this improved picture, relying on the type notion of a semigroup, we found that the number of semigroups of genus $g$ and type $t$ is constant when $t$ is close to $g$ while $g$ grows. We also study the unimodularity of various sequences as well as the behavior of the leaves in $\mathcal T$. We put forward several conjectures that are supported by various computational experiments.

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Dates et versions

hal-05184427 , version 1 (30-07-2025)
hal-05184427 , version 2 (25-11-2025)

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Jonathan Chappelon, Jorge Luis Ramírez Alfonsín, Dumitru I. Stamate. Numerical semigroup tree: type-representation. 2025. ⟨hal-05184427v1⟩
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