Complexity of straightening bideterminants (#P-hardness conjecture)

Determine the computational complexity of straightening bideterminants, i.e., of expanding a non-standard bitableau into a linear combination of standard bideterminants in the bideterminant ASL on a polynomial ring, and test the conjecture that this problem is #P-hard.

Background

Straightening bideterminants underlies many computations in the bideterminant ASL, but its formal complexity has not been established. The authors conjecture a #P-hard lower bound, motivated by the combinatorial structure of straightening and analogies with related #P-hard problems on Young tableaux.