TASEP and Planar Binary Trees: A Combinatorial Approach
  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. 
Xiangyu Cao
math.CO cond-mat.stat-mech