In this paper we introduce a particular semigroup transform A that fixes the invariants involved in Wilf's conjecture, except the embedding dimension. It also allows one to arrange the set of non-ordinary and non-irreducible numerical semigroups in a family of rooted trees. In addition, we study another transform, having similar features, that has been introduced by Bras-Amoros, and we make a comparison of them. In particular, we study the behavior of the embedding dimension under the action of such transforms, providing some consequences concerning Wilf's conjecture.
On Some Numerical Semigroup Transforms
Cisto C.
2022-01-01
Abstract
In this paper we introduce a particular semigroup transform A that fixes the invariants involved in Wilf's conjecture, except the embedding dimension. It also allows one to arrange the set of non-ordinary and non-irreducible numerical semigroups in a family of rooted trees. In addition, we study another transform, having similar features, that has been introduced by Bras-Amoros, and we make a comparison of them. In particular, we study the behavior of the embedding dimension under the action of such transforms, providing some consequences concerning Wilf's conjecture.File in questo prodotto:
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