Numerical semigroups with embedding dimension three and minimal catenary degree

Abstract

We characterize numerical semigroups $S$ with embedding dimension three attaining equality in the inequality $\max \Delta (S)+2\le \mathrm{cat}(S)$, where $\Delta (S)$ denotes the Delta set of $S$ and $\mathrm{cat}(S)$ denotes the catenary degree of $S$.