Zhang-zhang polynomials of multiple zigzag chains

Johanna Langner, Henryk A. Witek*, Grzegorz Mos

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)245-265
Number of pages21
JournalMatch
Volume80
Issue number1
StatePublished - 1 Jan 2018

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