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We define a family of asymmetric processes for particles on a one-dimensional
lattice, depending on a continuous parameter $\lambda \in [0,1]$, interpolating
between the completely asymmetric processes [1] (for $\lambda=1$) and the $n=1$
drop-push models [2] (for $\lambda=0$). For arbitrary $\lambda$, the model
describes an exclusion process, in which a particle pushes its right
neighbouring particles to the right, with rates depending on the number of
these particles. Using the Bethe ansatz, we obtain the
exact solution of the master equation.
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