Bidimensional unimodality conjecture for the Links–Gould polynomial of alternating links

Demonstrate that for any alternating link L, if LG(L; t0, t1) = Σ_{i,j} a_{ij} t0^i t1^j, then the two-indexed array (|a_{ij}|) is unimodal in the bidimensional sense: for every threshold K ≥ 0, the set of lattice points {(i,j) ∈ Z^2 : |a_{ij}| ≥ K} has no interior zeros with respect to its integer convex hull.

Background

The authors introduce a two-dimensional notion of unimodality tailored to the coefficient array of the two-variable Links–Gould polynomial. They conjecture that this bidimensional unimodality holds for all alternating links, mirroring long-standing conjectures for the one-variable Alexander polynomial but in a higher-dimensional coefficient setting.