The aim of this work is to exhibit a decomposition of partitions of natural numbers and numerical sets. In particular, we obtain a decomposition of a sparse numerical set into the so called hook semigroups which turn out ...

The aim of this work is to exhibit some relations between partitions of natural numbers and Arf semigroups. We also give characterizations of Arf semigroups via the hook-sets of Young tableaux of partitions.

The aim of this work is to exhibit the relationship between the Arf closure of a numerical semigroup S and its Lipman semigroup L(S). This relationship is then used to give direct proofs of some characterizations of Arf ...