5 problems

commonly reducible when $\lambda^{\bullet}$ and $\mu^{\bullet}$ are obtained by choosing common columns of $\lambda$ and $\mu$. Common reducibility conjecture. If $\lambda_1>r$, th…

Stretching quasi-polynomial conjecture. If $\lambda_2$ and $\beta_2$ are both even, then $\mathrm{mult}_{s\lambda}(s\beta)$ is a polynomial in $s$ when $\kappa_1$ is even and, exce…

Folding-square conjecture. The number of such triplets is a square integer: there is an integer $m$ such that

Let $p$ be prime, let $e<f$ be positive integers, and set $m=p^e$, $n=p^f$, and $k=n/m=p^{f-e}$. Let $M^{se}$ and $M^{es}$ denote the change-of-basis matrices between the Schur and…

Let $\lambda$ and $\mu$ be partitions of the same size. Write $a(\lambda,\mu)$ and $b(\lambda,\mu)$ for the associated invariants introduced in the paper, with $b(\lambda,\mu)$ the…