We recall L-shapes, which are minimal distance diagrams, related to weighted 2-Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we consider some classes of numerical semigroups useful in the study of curve singularity. Then, we associate L-shapes to each numerical 3-semigroup and we describe some main invariants of numerical 3-semigroups in terms of their associated L-shapes. Finally, we give a characterization of the parameters of the L-shapes associated with a numerical 3-semigroup in terms of its generators, and we use it to classify the numerical 3-semigroups of interest in curve singularity.

Peer Reviewed