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.

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Acknowledgements

This work was supported partially by the National Natural Science Foundation of China (Nos. 11771065, 11871304), the Young Talents Invitation Program of Shandong Province.

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Correspondence to Yi Wang.

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Li, G., Liu, L.L. & Wang, Y. Analytic properties of sextet polynomials of hexagonal systems. J Math Chem (2021). https://doi.org/10.1007/s10910-021-01213-x

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Keywords

  • Hexagonal system
  • Sextet polynomial
  • Real zero
  • Unimodal
  • Log-concavity

Mathematics Subject Classification

  • 05C31
  • 92E10
  • 26C10