7 problems

Let $E$ and $E'$ be skew diagrams. For skew-diagram composition, consider factorizations … and the analogous expression for $E'$. For $i=2,\ldots,r$, require $E_i=W_iO_iW_i$ to sat…

For a skew diagram $F$, write $F^t$ for its transpose and $F\sim F^t$ when their skew Schur functions agree. Let $D\circ_W E$ denote the paper's skew-diagram composition, where…

A skew diagram is a finite diagram whose skew Schur function is denoted by $s_D$; two skew diagrams $D$ and $D'$ are skew-equivalent when $s_D=s_{D'}$, written $D\sim D'$. The skew…

Tilde-operation conjecture for skew Schur functions. For all $\mu/\alpha$ and $\nu/\beta$, if $(\mu/\alpha,\nu/\beta)^\sim=(\lambda/\sigma,\rho/\tau)$, then

Fomin–Fulton–Li–Poon conjecture for skew partitions. For any skew partitions $\mu/\alpha$ and $\nu/\beta$, if

McNamara–van Willigenburg's conjecture. The diagrams $\mathcal{D}$ and $\mathcal{E}$ satisfy $\mathcal{D}\sim\mathcal{E}$ if and only if the factors satisfy:…

Let skew diagrams be considered up to equality of their skew Schur functions, and call the resulting sets of mutually equivalent diagrams equivalence classes. Power-of-two conjectu…