Log-concavity conjecture for sextet polynomials

Let $H$ be a hexagonal system, and let its sextet polynomial be the polynomial whose coefficients count sextet-related structures of $H$. Log-concavity conjecture for sextet polynomials. The sextet polynomial of a hexagonal system has log-concave coefficients. The authors present this as a stronger conjecture than Gutman's unimodality conjecture; it is stated as an open direction for general hexagonal systems.