Analytic Properties of Forcing and Anti-Forcing Polynomials of Pyrene Chains

In this paper we investigate analytic properties of forcing and anti-forcing polynomials of pyrene chains. We show that zeros of the forcing polynomials $$F(P_n, x)$$ are real, located in the interval $$(-1, 0]$$ , and dense in the corresponding closed interval. We also show that the coefficients of $$F(P_n, x)$$ are unimodal, log-concave, and asymptotically normal. For anti-forcing polynomials $$Af(P_n, x)$$ , we show that the coefficients are unimodal and log-concave. Furthermore, the distribution of zeros of $$Af(P_n, x)$$ is also investigated.