Classical output-sensitive algorithm conjecture for Littlewood–Richardson coefficients

Let $\bla$, $\bmu$, and $\bnu$ be partitions such that $|\bla|=|\bmu|+|\bnu|$. Littlewood–Richardson algorithm conjecture. There exists a classical algorithm running in time

$$O\left(\frac{f^\bla}{f^\bmu f^\bnu}\operatorname{poly}(n)\right)$$

that computes the Littlewood–Richardson coefficient $c^\bla_{\bmu\bnu}$. The conjecture is a proposed classical counterpart to the known quantum runtime, with polynomial-time algorithms already available in some restricted cases such as fixed $ell(\bla)$; the general case remains open.