We give a simple explanation why the stationary state of the 1D TASEP model with open boundaries is related to the Catalan numbers. Our construction is based on planar binary trees and provides a combinatorial solution of the stationary state. We discuss the relation to Catalan tableaux approaches in an appendix.
A combinatorial approach to scattering diagrams
Order structure on the algebra of permutations and of planar binary trees
A combinatorial approach to the power of 2 in the number of involutions
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