Zhang-zhang polynomials of multiple zigzag chains

Johanna Langner; Henryk A. Witek; Grzegorz Mos

Zhang-zhang polynomials of multiple zigzag chains

Johanna Langner
, Henryk A. Witek^*
, Grzegorz Mos

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

Generating functions of the Zhang-Zhang polynomials of multiple zigzag chains Z(m; n) and generalized multiple zigzag chains Z_κ(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, Σ^∞ _m=0 ZZ(Z(m; n); z)t^m = [0;-T; (-1)²zt; (-1)³zt; ⋯ ; (-1)ⁿzt; 1 + (-1)ⁿ⁺¹zt]; or, in the case of Z_κ(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.

Original language	English
Pages (from-to)	245-265
Number of pages	21
Journal	Match
Volume	80
Issue number	1
State	Published - Jan 2018

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https://match.pmf.kg.ac.rs/electronic_versions/Match80/n1/match80n1_245-265.pdf

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title = "Zhang-zhang polynomials of multiple zigzag chains",

abstract = "Generating functions of the Zhang-Zhang polynomials of multiple zigzag chains Z(m; n) and generalized multiple zigzag chains Zκ(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, Σ∞ m=0 ZZ(Z(m; n); z)tm = [0;-T; (-1)2zt; (-1)3zt; ⋯ ; (-1)nzt; 1 + (-1)n+1zt]; or, in the case of Zκ(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.",

author = "Johanna Langner and Witek, \{Henryk A.\} and Grzegorz Mos",

year = "2018",

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AU - Langner, Johanna

AU - Witek, Henryk A.

AU - Mos, Grzegorz

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N2 - Generating functions of the Zhang-Zhang polynomials of multiple zigzag chains Z(m; n) and generalized multiple zigzag chains Zκ(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, Σ∞ m=0 ZZ(Z(m; n); z)tm = [0;-T; (-1)2zt; (-1)3zt; ⋯ ; (-1)nzt; 1 + (-1)n+1zt]; or, in the case of Zκ(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.

AB - Generating functions of the Zhang-Zhang polynomials of multiple zigzag chains Z(m; n) and generalized multiple zigzag chains Zκ(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, Σ∞ m=0 ZZ(Z(m; n); z)tm = [0;-T; (-1)2zt; (-1)3zt; ⋯ ; (-1)nzt; 1 + (-1)n+1zt]; or, in the case of Zκ(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.

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SN - 0340-6253

VL - 80

SP - 245

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JO - Match

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Zhang-zhang polynomials of multiple zigzag chains

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