  We give two combinatorial interpretations of the Matrix Ansatz of the PASEP
in terms of lattice paths and rook placements. This gives two (mostly)
combinatorial proofs of a new enumeration formula for the partition function of
the PASEP. Besides other interpretations, this formula gives the generating
function for permutations of a given size with respect to the number of ascents
and occurrences of the pattern 13-2, the generating function according to weak
exceedances and crossings, and the n-th moment of certain q-Laguerre
polynomials.
