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. It is demonstrated that the considered correlation functions under different boundary conditions are the exponential generating functions of various types of paths, in particular, Dyck and Motzkin paths.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 487, 2019, pp. 53–67.
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Bogoliubov, N.M. Enumerative Combinatorics of XX0 Heisenberg Chain. J Math Sci 257, 459–468 (2021). https://doi.org/10.1007/s10958-021-05494-0
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DOI: https://doi.org/10.1007/s10958-021-05494-0