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Discrete Mathematics & Theoretical Computer Science |
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 $n^{\mathrm{th}}$ moment of certain $q$-Laguerre polynomials.
Source : ScholeXplorer
IsRelatedTo ARXIV cond-mat/0312457 Source : ScholeXplorer IsRelatedTo DOI 10.1088/0305-4470/37/18/006 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.cond-mat/0312457
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