Matrix Ansatz , lattice paths and rook placements

  title={Matrix Ansatz , lattice paths and rook placements},
  author={Sylvie Corteel and Matthieu Josuat-Verg{\`e}s and Thomas Prellberg and Martin Rubey},
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
9 Extracted Citations
33 Extracted References
Similar Papers

Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 33 references

A bijective proof of a Touchard-Riordan f ormula

  • J.-G. Penaud
  • Disc. Math., Vol. 139
  • 1995
Highly Influential
6 Excerpts

Exact soluti on of a 1D asymmetric exclusion model using a matrix formulation

  • B. Derrida, M. Evans, V. Hakim, V. Pasquier
  • J. Phys. A: Math. Gen. 26
  • 1993
Highly Influential
7 Excerpts

Alternative tableaux and permutations

  • X. G. Viennot
  • i preparation
  • 2008
Highly Influential
3 Excerpts

Permutation tablea ux and permutation patterns

  • E. Steingrı́msson, L. K. Williams
  • J. Combin. Theory Ser. A, Vol
  • 2007
Highly Influential
5 Excerpts

Total positivity

  • A. Postnikov
  • Grassmannians, and ne tworks, Preprint
  • 2006
Highly Influential
3 Excerpts

Alternative tableaux and partially asym metric exclusion process

  • X. G. Viennot
  • preparation
  • 2008
1 Excerpt

Combinato rial Hopf algebras

  • J. C. Novelli, J-Y. Thibon, L. K. Williams
  • noncommutative Hall- Littlewood functions, and…
  • 2008
1 Excerpt

Similar Papers

Loading similar papers…