Geodesic
Scalar product of the five-vertex model and complete symmetric polynomials
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 29, Tome 520 (2023), pp. 124-138

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The scalar product of the state-vectors of the exactly solvable five-vertex model with the fixed boundary conditions is considered. Various relations including those in terms of complete symmetric polynomials are derived. The limiting forms of the obtained answers may be interpreted in terms of random walks on a square grid. 
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     author = {N. M. Bogolyubov and C. L. Malyshev},
     title = {Scalar product of the five-vertex model and complete symmetric polynomials},
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N. M. Bogolyubov; C. L. Malyshev. Scalar product of the five-vertex model and complete symmetric polynomials. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 29, Tome 520 (2023), pp. 124-138. http://geodesic.mathdoc.fr/item/ZNSL_2023_520_a3/