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In this note, we consider the six-vertex model with domain wall boundaryconditions, defined on a $M\times M$ lattice, in the inhomogeneous case wherethe partition function depends on 2M inhomogeneities $\lambda_j$ and $\mu_k$.For a particular choice of the set of $\lambda_j$ we find a new determinantrepresentation for the partition function, which allows evaluation of the bulkfree energy in the thermodynamic limit. This provides a new connection betweentwo types of determinant formulae. We also show in a special case that spincorrelations on the horizontal line going through the center coincide with theones for periodic boundary conditions.

Inhomogeneous six-vertex model with domain wall boundary conditions and Bethe ansatz