Analytic properties of sextet polynomials of hexagonal systems

In this paper we investigate analytic properties of sextet polynomials hexagonal systems. For the pyrene chains, show that zeros $$P_n(x)$$ are real, located in open interval $$(-3-2\sqrt{2},-3+2\sqrt{2})$$ and dense corresponding closed interval. We also coefficients symmetric, unimodal, log-concave, asymptotically normal. general systems, real all $$(-\infty ,0]$$ , conjecture every polynomial has log-concave coefficients.