  The representation of the Bethe wave functions of certain integrable models
via the Schur functions allows to apply the well-developed theory of the
symmetric functions to the calculation of the thermal correlation functions.
The algebraic relations arising in the calculation of the scalar products and
the correlation functions are based on the Binet-Cauchy formula for the Schur
functions. We provide a combinatorial interpretation of the formula for the
scalar products of the Bethe state-vectors in terms of nests of the
self-avoiding lattice paths constituting the so-called watermelon
configurations. The interpretation proposed is, in its turn, related to the
enumeration of the boxed plane partitions.
