TY - JOUR

T1 - Hexagonal flakes as fused parallelograms

T2 - A determinantal formula for Zhang-Zhang polynomials of the O(2, m, n) benzenoids

AU - He, Bing Hau

AU - Langner, Johanna

AU - Witek, Henryk Arnold

N1 - Publisher Copyright:
© 2021 The Chemical Society Located in Taipei & Wiley-VCH GmbH

PY - 2021/2

Y1 - 2021/2

N2 - We report a determinantal formula for the Zhang-Zhang polynomial of the hexagonal flake O(2, m, n) applicable to arbitrary values of the structural parameters m and n. The reported equation has been discovered by extensive numerical experimentation and is given here without a proof. Our combinatorial analysis performed on a large collection of isostructural O(2, m, n) benzenoids yielded a ZZ polynomial formula corresponding to the determinant of a certain 2 × 2 matrix referred to by us as the generalized John–Sachs path matrix, because of the striking structural similarity with the original path matrices introduced by the John–Sachs theory of Kekulé structures. The presented conjecture hints at the existence of a generalization of the John–Sachs theory applicable to characterization and enumeration of Clar covers.

AB - We report a determinantal formula for the Zhang-Zhang polynomial of the hexagonal flake O(2, m, n) applicable to arbitrary values of the structural parameters m and n. The reported equation has been discovered by extensive numerical experimentation and is given here without a proof. Our combinatorial analysis performed on a large collection of isostructural O(2, m, n) benzenoids yielded a ZZ polynomial formula corresponding to the determinant of a certain 2 × 2 matrix referred to by us as the generalized John–Sachs path matrix, because of the striking structural similarity with the original path matrices introduced by the John–Sachs theory of Kekulé structures. The presented conjecture hints at the existence of a generalization of the John–Sachs theory applicable to characterization and enumeration of Clar covers.

KW - Clar covering polynomials

KW - Clar covers

KW - hexagonal flakes

KW - ZZ polynomials

UR - http://www.scopus.com/inward/record.url?scp=85093652475&partnerID=8YFLogxK

U2 - 10.1002/jccs.202000420

DO - 10.1002/jccs.202000420

M3 - Article

AN - SCOPUS:85093652475

SN - 0009-4536

JO - Journal of the Chinese Chemical Society

JF - Journal of the Chinese Chemical Society

ER -