Matrix Ansatz , lattice paths and rook placements

@inproceedings{Corteel2008MatrixA,
  title={Matrix Ansatz , lattice paths and rook placements},
  author={Sylvie Corteel and Matthieu Josuat-Verg{\`e}s and Thomas Prellberg and Martin Rubey},
  year={2008}
}
We give two combinatorial interpretations of the Matrix Ans atz 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 occurren ces of the pattern 13-2, the generating function according to weak exceedances and crossings, and the… CONTINUE READING
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