We conjecture an exact expression for the large deviation function of the
stationary state current in the partially asymmetric exclusion process with
periodic boundary conditions. This expression is checked for small systems
using functional Bethe Ansatz. It generalizes a previous result by Derrida and
Lebowitz for the totally asymmetric exclusion process, and gives the known
values for the three first cumulants of the current in the partially asymmetric
model. Our result is written in terms of tree structures and provides a new
example of a link between integrable models and combinatorics.Comment: 7 page