Browsing by Author "Mos, Grzegorz"

Now showing 1 - 3 of 3

Zhang-Zhang Polynomials of Multiple Zigzag Chains
(2018-01-01)
Langner, Johanna
;
Witek, Henryk A.
;
Mos, Grzegorz
;
應用化學系
;
應用化學系分子科學碩博班
Generating functions of the Zhang-Zhang polynomials of multiple zigzag chains Z(m, n) and generalized multiple zigzag chains Z(k)(m, n) are derived for arbitrary values of the indices. These generating functions can be expressed in the form of highly regular finite continued fractions, Sigma(infinity)(m=0) ZZ(Z(m, n),z)t(m) = [0; -t,(-1)(2)zt,(-1)(3)zt,&,(-1)(n)zt, 1 + (-1)(n+1) zt], or, in the case of Z(k)(m, n), products of such continued fractions. For the particularly important case of the multiple zigzag chains Z(m, n), the generating functions are expanded to yield a closed form for the Zhang-Zhang polynomials of multiple zigzag chains Z(m, n) that is valid for arbitrary values of m and n.
Zhang-Zhang Polynomials of Regular 3-and 4-tier Benzenoid Strips
(2015-01-01)
Witek, Henryk A.
;
Mos, Grzegorz
;
Chou, Chien Pin
;
應用化學系
;
應用化學系分子科學碩博班
We present compact, closed-form expressions for Zhang-Zhang (ZZ) polynomials of regular 3- and 4-tier benzenoid strips. It is possible to unify the ZZ polynomials of 11 classes of regular 3- and 4-tier benzenoid strips into a single, universal, three-parameter formula Sigma(Cl)(k=0) Sigma(2)(l=0) a(l) (n +1(k)) (n - l + Cl - k n-1)x(k) where Cl is an element of{2,3,4,5,6}, a(0) = 1, a(1) is an element of{0,1,2,3}, and a(2) is an element of{0,1}. The parameters a(1) and a(2) partition the 3- and 4-tiers benzenoid strips into four superfamilies; a(1) and a(2) are constant within a given superfamily and Cl enumerates subsequent benzenoid structures. Our finding provides also a compact and universal expression for the number of Kekule structures for regular 3- and 4-tier benzenoid strips given by K = Sigma(2)(l=0) a(l)(n - l + Cl Cl) These expressions are expected to be readily applicable also to wider regular benzenoid strips.
Zhang-Zhang Polynomials of Regular 5-tier Benzenoid Strips
(2017-01-01)
Witek, Henryk A.
;
Langner, Johanna
;
Mos, Grzegorz
;
Chou, Chien-Pin
;
應用化學系
Formal derivations of closed-form expressions for Clar covering polynomials (aka Zhang Zhang polynomials or ZZ polynomials) of twelve classes of regular 5-tier benzenoid strips are presented. The derived formulas, together with the results reported previously in the literature, complete the full collection of ZZ polynomial formulas for the regular 5-tier benzenoid strips.