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The trigonometric six-vertex model with domain wall boundary conditions andone partially reflecting end on a lattice of size $2n\times m$, $m\leq n$, isconsidered. The partition function is computed using the Izergin-Korepinmethod, generalizing the result of Foda and Zarembo from the rational to thetrigonometric case. Thereafter we specify the parameters in Kuperberg's way toget a formula for the number of states as a determinant of Wilson polynomials.We relate this to a type of ASM-like matrices.

Exact results for the six-vertex model with domain wall boundary conditions and a partially reflecting end