On the number of numerical semigroups of prime power genus

Shalom Eliahou, Jorge Ramirez Alfonsin

Given $g\ge 1$, the number $n(g)$ of numerical semigroups $S\subset \mathbb{N}$ of genus $|\mathbb{N}\setminus S|$ equal to $g$ is the subject of challenging conjectures of Bras-Amorós. In this…