2 problems

Residue-class unimodality conjecture. For every residue class $r$, $0\leq r<a$, the coefficients of $q^{ak+r}$ in $\mathbf{Cat}_{a,b}(q)$ are unimodal. The conjecture refines ordin…

Coset age conjecture. There is an age function $\iota$ on the cosets $\mathfrak{c}\in\boldsymbol{\Lambda}/\boldsymbol{\Lambda}_T$ such that