S. Corteel ; M. Josuat-Vergès ; T. Prellberg ; M. Rubey - Matrix Ansatz, lattice paths and rook placements

dmtcs:2751 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2751
Matrix Ansatz, lattice paths and rook placementsArticle

Authors: S. Corteel 1; M. Josuat-Vergès ORCID1; T. Prellberg 2; M. Rubey 3

  • 1 Laboratoire de Recherche en Informatique
  • 2 School of Mathematical Sciences [Queen Mary]
  • 3 Institut für Algebra, Zahlentheorie und Diskrete Mathematik

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.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Enumeration,Permutation tableaux,Rook placements,Lattice paths,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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