Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Mandelshtam Olya

Rhombic alternative tableaux, assemblees of permutations, and the ASEP
Olya Mandelshtam  1  , Xavier Viennot  2  
1 : Department of Mathematics, University of California, Berkeley, USA
2 : Laboratoire Bordelais de Recherche en Informatique  (LaBRI)  -  Website
Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Centre National de la Recherche Scientifique : UMR5800
Domaine Universitaire 351, cours de la Libération 33405 Talence Cedex -  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 assemblees. 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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