Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Wednesday 6
Cedric Chauve
› 10:00 - 10:30 (30min)
› Djavad Mowafaghian Cinema
Rhombic alternative tableaux, assembl ´ees of permutations, and the ASEP
Olya Mandelshtam  1  , Xavier Viennot  2  
1 : Department of Mathematics, University of California, Berkeley, USA
2 : LABRI, CNRS, Université de Bordeaux, Bordeaux, France
Centre national de la recherche scientifique - CNRS (France)

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.

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