Polynomial-time computation for hook-shaped Kronecker coefficients

Establish a polynomial-time algorithm for computing g(λ, μ, ν) when ν = (n − a, 1^a) is a hook and λ and μ have Durfee square sizes at most a fixed constant k.

Background

The paper notes that Kronecker coefficients are polynomially bounded when all three partitions have fixed Durfee square size, but computing their exact values remains difficult because existing approaches involve exponentially large alternating sums or exponentially many tableaux. The hook case is identified as a particularly simple unresolved instance: the hook partition ν has the form (n − a, 1^a), while λ and μ have bounded diagonal lengths.