# Punctured plane partitions and the q-deformed Knizhnik-Zamolodchikov and Hirota equations - Mathematics > Combinatorics

Abstract: We consider partial sum rules for the homogeneous limit of the solution ofthe q-deformed Knizhnik-Zamolodchikov equation with reflecting boundaries inthe Dyck path representation. We show that these partial sums arise in asolution of the discrete Hirota equation, and prove that they are thegenerating functions of $\tau^2$-weighted punctured cyclically symmetrictranspose complement plane partitions where $\tau=-q+q^{-1}$. In the cases ofno or minimal punctures, we prove that these generating functions coincide with$\tau^2$-enumerations of vertically symmetric alternating sign matrices andmodifications thereof.

Author: Jan de Gier, Pavel Pyatov, Paul Zinn-Justin

Source: https://arxiv.org/