Full equivalence class criterion for ribbons

Let $\alpha=(\alpha_1,\alpha_2,\ldots,\alpha_m)$ be a ribbon with $\alpha_1\geq\alpha_2\geq\cdots\geq\alpha_m$, where each $\alpha_i\geq2$ and $m\geq3$. Let $N_j$ denote the quantity defined in the necessary condition of the paper. Full equivalence class conjecture. The ribbon $\alpha$ has full equivalence class if and only if

$$N_j<\sum_{i=j+1}^m\alpha_i-(m-j-2)$$

for all $1\leq j\leq m-2$. This conjectures that the necessary condition established in the paper is also sufficient; it is known for ribbons with three or four rows and has been verified computationally in the stated cases for five, six, and seven rows.