Combinatorial interpretation of Kronecker coefficients via bitableaux

Prove that each Kronecker coefficient is equal to the number of lexicographic bitableaux of the specified shape and weights whose two associated reading words satisfy the required pair of Yamanouchi conditions.

Background

The paper introduces lexicographic bitableaux as combinatorial fillings whose entries are ordered pairs and associates two weights and two reading-word constructions to each object. The motivating goal is to interpret the Kronecker coefficients, which are the multiplicities appearing in the decomposition of tensor products or, equivalently, in the Kronecker coproduct of Schur functions.

The conjecture proposes that imposing Yamanouchi conditions on both reading words would select objects counted by the Kronecker coefficients. The paper constructs only a crystal structure associated with one reading word and explicitly identifies the extraction of the second reading word as unresolved, so the conjecture is not established.