Frögoh"amosa conjecture on equality in Wilf's inequality

Let $\Gamma\neq\mathbb{N}$ be a numerical semigroup. Write $c(\Gamma)$ for its conductor, $e(\Gamma)$ for its embedding dimension, and $\delta(\Gamma)$ for its delta-invariant. For positive integers $m,q$ with $m>1$, define

$$W_{m,q}:=\{0,m,2m,3m,\ldots,(q-1)m,qm,qm+1,qm+2,\ldots\}.$$

Frögoh"amosa conjecture. The equality

$$c(\Gamma)=e(\Gamma)\cdot\delta(\Gamma)$$

holds if and only if $\Gamma$ has embedding dimension $2$ or there exist $m,q\in\mathbb{N}\setminus\{0\}$ with $m>1$ such that $\Gamma=W_{m,q}$.

The conjecture characterizes the numerical semigroups attaining equality in Wilf's inequality. The paper reports many known particular cases and presents the statement as open.