On certain combinatorial expressions of TASEP transition probabilities (opens in new tab)

We study combinatorial structures arising from finite-time transition probabilities of the Totally Asymmetric Simple Exclusion Process with open boundary conditions. While much of the existing combinatorial theory regarding the TASEP concerns the steady-state distribution, we focus instead on the transient dynamics. We first show that the enumeration of transition sequences between two configurations of the open TASEP is equivalent to the enumer...