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Matrix Ansatz, lattice paths and rook placements

Sylvie Corteel, Matthieu Josuat-Verges, Thomas Prellberg, and Martin Rubey
Arxiv ID: 0811.4606Last updated: 1/26/2021
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.

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