Analytic properties of sextet polynomials of hexagonal systems

Abstract

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