Lorentzian property for homogenized Alexander polynomials of all alternating links

Show that for every alternating link L, the homogenized polynomial Homog(Δ_L(−t)) is denormalized Lorentzian, equivalently that the coefficient sequence of Δ_L(t) is log-concave with no internal zeros.

Background

Leveraging connections between Lorentzian polynomials and log-concavity, the paper proves equivalence between the denormalized Lorentzian property of the homogenized Alexander polynomial and the Stoimenow conjecture. Computations verify the property for alternating knots up to 16 crossings; the authors note it is conjecturally true in full generality.

References

Thus, following Stoimenow the Alexander polynomial satisfies the Lorentzian property for all alternating knots with up to 16 crossings, and this is conjecturally true for all alternating links.

— On some log-concavity properties of the Alexander-Conway and Links-Gould invariants (2509.16868 - Harper et al., 21 Sep 2025) in Section 4, following Proposition 4.2