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arXiv · 1912.03680

Analytic properties of sextet polynomials of hexagonal systems

Guanru Li·Lily Li Liu·Yi Wang
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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.

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Guanru Li, Lily Li Liu, Yi Wang. 2019-12-10. Analytic properties of sextet polynomials of hexagonal systems. https://arxiv.org/abs/1912.03680

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