Enumerative combinatorics of $XX0$ Heisenberg chain

In the present paper the enumeration of a certain class of directed lattice paths is based on the analysis of dynamical correlation functions of the exactly solvable $XX0$ model. This model is the zero anisotropy limit of one of the basic models of the theory of integrable systems, the $XXZ$ Heisenberg magnet. We demonstrate that the considered correlation functions under different boundary conditions are the exponential generating functions of the different types of paths, Dyck and Motzkin in particular.