## 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)^{2}zt; (-1)^{3}zt; ⋯ ; (-1)^{n}zt; 1 + (-1)^{n+1}zt]; 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 |
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Pages (from-to) | 245-265 |

Number of pages | 21 |

Journal | Match |

Volume | 80 |

Issue number | 1 |

State | Published - 1 Jan 2018 |