3 problems

Near-equality classification conjecture. Up to reversal of $\alpha$ and $\beta$, the compositions $\alpha$, $\beta$ and partition $\nu$ are one of the five cases of Theorem 1.1, on…

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 quanti…

Equality characterization conjecture. For ribbons $\alpha,\beta$, one has $\rho_\alpha=\rho_\beta$ if and only if there exist $j,k,ell$ such that