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The raise and peel model of a one-dimensional fluctuating interface (model A)is extended by considering one source (model B) or two sources (model C) at theboundaries. The Hamiltonians describing the three processes have, in thethermodynamic limit, spectra given by conformal field theory. The probabilityof the different configurations in the stationary states of the three modelsare not only related but have interesting combinatorial properties. We showthat by extending Pascal's triangle (which gives solutions to linear relationsin terms of integer numbers), to an hexagon, one obtains integer solutions ofbilinear relations. These solutions give not only the weights of the variousconfigurations in the three models but also give an insight to the connectionsbetween the probability distributions in the stationary states of the threemodels. Interestingly enough, Pascal's hexagon also gives solutions to aHirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few  references are adde

Raise and peel models of fluctuating interfaces and combinatorics of Pascal s hexagon