  We consider the raise and peel model of a one-dimensional fluctuating
interface in the presence of an attractive wall. The model can also describe a
pair annihilation process in a disordered unquenched media with a source at one
end of the system. For the stationary states, several density profiles are
studied using Monte Carlo simulations. We point out a deep connection between
some profiles seen in the presence of the wall and in its absence. Our results
are discussed in the context of conformal invariance ($c = 0$ theory). We
discover some unexpected values for the critical exponents, which were obtained
using combinatorial methods.
  We have solved known (Pascal's hexagon) and new (split-hexagon) bilinear
recurrence relations. The solutions of these equations are interesting on their
own since they give information on certain classes of alternating sign
matrices.
