Classical computation of general plethysm coefficients

Determine whether, for partitions λ ⊢ n, μ ⊢ d, and ν ⊢ m with n = dm, there exists a classical algorithm computing the plethysm coefficient a^λ_{μ,ν} in time O(f^λ (f^ν)^d f^μ poly(n)).

Background

The paper develops polynomial-time algorithms for important plethysm families, especially coefficients a^λ_{d,m} when the outer partition is a single row and either its size and the length of λ are fixed or f^λ is polynomially bounded.

The proposed question asks whether the runtime of the quantum algorithm studied in the cited work can always be matched, up to a polynomial factor, by a classical algorithm. A positive answer would eliminate the possibility of a superpolynomial quantum advantage for the relevant plethysm computations.