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We present the solution of a linear Restricted Solid--on--Solid (RSOS) modelin a field. Aside from the origins of this model in the context of describingthe phase boundary in a magnet, interest also comes from more recent work onthe steady state of non-equilibrium models of molecular motors. While similarto a previously solved (non-restricted) SOS model in its physical behaviour,mathematically the solution is more complex. Involving basic hypergeometricfunctions ${}_3\phi_2$, it introduces a new form of solution to the lexicon ofdirected lattice path generating functions.

Exact Solution of the Discrete (1+1)-dimensional RSOS Model with Field and Surface Interactions