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arXiv · 2209.05803

On some numerical semigroup transforms

Carmelo Cisto
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Abstract

In this paper we introduce a particular semigroup transform $\mathcal{A}$ that fixes the invariants involved in Wilf's conjecture, except the embedding dimension. It also allows one to arrange the set of not ordinary and not irreducible numerical semigroups in a family of rooted trees. We study also another transform, having similar features, that has been introduced by Bras-Amorós, and we make a comparison of them. In particular we study the behaviour of the embedding dimension under the action of such transforms, providing some consequences concerning Wilf's conjecture.

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Carmelo Cisto. 2022-09-13. On some numerical semigroup transforms. https://doi.org/10.1142/s1005386722000384

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