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We study the combinatorics of the change of basis of three representations ofthe stationary state algebra of the two parameter simple asymmetric exclusionprocess. Each of the representations considered correspond to a different setof weighted lattice paths which, when summed over, give the stationary stateprobability distribution. We show that all three sets of paths arecombinatorially related via sequences of bijections and sign reversinginvolutions.

Simple Asymmetric Exclusion Model and Lattice Paths: Bijections and Involutions