The bitableaux conjecture for Kronecker coefficients

Let $$ be a partition, and let lexicographic bitableaux be the combinatorial objects introduced in the paper, with prescribed shape and weights. A reading word is Yamanouchi when it satisfies the usual lattice-word condition.

Bitableaux conjecture. The Kronecker coefficient with the corresponding partitions is counted by lexicographic bitableaux of the given shape and weights whose pair of reading words are both Yamanouchi.

A positive combinatorial interpretation of Kronecker coefficients is a long-standing open problem in combinatorial representation theory. The conjecture is motivated by the role of lexicographic bitableaux as a possible generalization of the RSK and dual RSK insertion algorithms.