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 $\maxΔ(S)+2\leq \operatorname{cat}(S)$, where $Δ(S)$ denotes the Delta set of $S$ and $\operatorname{cat}(S)$ denotes the catenary degree of $S$.

Theorems & Definitions (14)

• Theorem 2.1
• Theorem 2.2
• Theorem 2.3: CT
• Example 2.4
• Theorem 3.1
• Proposition 3.2
• Proposition 3.3
• Proposition 3.4
• Theorem 3.5
• Theorem 3.6: NS