Zhang–Zhang's unimodality conjecture for Clar covering polynomials

Let $H$ be a hexagonal system, and let its Clar covering polynomial be

$$\chi(H,x)=\sum_{k=0}^{C(H)}c(H,k)x^k,$$

where $c(H,k)$ is the number of Clar covers of $H$ having precisely $k$ hexagons. Zhang–Zhang's unimodality conjecture. The Clar covering polynomial of a hexagonal system has unimodal coefficients. Zhang and Zhang had established strict decrease for the higher-degree first-half coefficients; the full unimodality assertion remains a conjecture in the source.