Explicit correlation functions for the six-vertex model in the free-fermion regime

In this article, we show that, in the free-fermion regime of the six-vertex model, all $k$-point correlation functions of vertex types admit a determinantal representation: \begin{align*} \mathbb{P}\Bigg( \bigcap_{p=1}^k \{ \text{vertex at } v^p \text{ has type } t_p \} \Bigg) = \left( \prod_{p=1}^k