In this paper, we introduce the rhombic alternative tableaux, whose weight generating functions provide

combinatorial formulae to compute the steady state probabilities of the two-species ASEP. In the ASEP, there are

two species of particles, one heavy and one light, on a one-dimensional finite lattice with open boundaries, and the

parameters a,b, and q describe the hopping probabilities. The rhombic alternative tableaux are enumerated by the

Lah numbers, which also enumerate certain assembl´ees of permutations. We describe a bijection between the rhombic

alternative tableaux and these assembl´ees. We also provide an insertion algorithm that gives a weight generating

function for the assemb´ees. Combined, these results give a bijective proof for the weight generating function for the

rhombic alternative tableaux.

- Poster