Matrix Ansatz, lattice paths and rook placements
Combinatorics
2021-01-26 v1 Statistical Mechanics
Abstract
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.
Cite
@article{arxiv.0811.4606,
title = {Matrix Ansatz, lattice paths and rook placements},
author = {Sylvie Corteel and Matthieu Josuat-Verges and Thomas Prellberg and Martin Rubey},
journal= {arXiv preprint arXiv:0811.4606},
year = {2021}
}