. Bce-+-06-]-r, S. Brak, J. Corteel, R. Essam, A. Parviainen et al., A combinatorial derivation of the PASEP stationary state, Electron. J. Combin.Research Paper, vol.13, issue.23, p.pp, 2006.

J. [. Brak and . Essam, Asymmetric exclusion model and weighted lattice paths, Journal of Physics A: Mathematical and General, vol.37, issue.14, pp.4183-4217, 2004.
DOI : 10.1088/0305-4470/37/14/002

E. Babson and E. Steingrímsson, Generalized permutation patterns and a classification of the Mahonian statistics, Sém. Lothar. Combin, vol.44, issue.18, p.pp, 2000.

]. A. Bur07 and . Burstein, On some properties of permutation tableaux, 2007.

]. A. Cla01 and . Claesson, Generalized pattern avoidance, European J. Combin, vol.22, issue.7, pp.961-971, 2001.

T. [. Claesson and . Mansour, Counting occurrences of a??pattern of type (1,2) or (2,1) in permutations, Advances in Applied Mathematics, vol.29, issue.2, pp.293-310, 2002.
DOI : 10.1016/S0196-8858(02)00012-X

A. Claesson and T. Mansour, Enumerating permutations avoiding a pair of Babson- Steingrímsson patterns, Ars Combin, vol.77, pp.17-31, 2005.

P. [. Corteel and . Nadeau, Permutation tableaux and permutation descents, 2007.

]. S. Cor07 and . Corteel, Crossings and alignments of permutations, Adv. in Appl. Math, vol.38, issue.2, pp.149-163, 2007.

L. [. Corteel and . Williams, A Markov Chain on Permutations which Projects to the PASEP, International Mathematics Research Notices, p.609188, 2006.
DOI : 10.1093/imrn/rnm055

L. [. Corteel and . Williams, Tableaux combinatorics for the asymmetric exclusion process, Advances in Applied Mathematics, vol.39, issue.3, 2007.
DOI : 10.1016/j.aam.2006.08.002

E. [. Derrida, D. Domany, and . Mukamel, An exact solution of a one-dimensional asymmetric exclusion model with open boundaries, Journal of Statistical Physics, vol.54, issue.3-4, pp.3-4667, 1992.
DOI : 10.1007/BF01050430

M. [. Derrida, V. Evans, V. Hakim, and . Pasquier, Exact solution of a 1D asymmetric exclusion model using a matrix formulation, Journal of Physics A: Mathematical and General, vol.26, issue.7, pp.1493-1517, 1993.
DOI : 10.1088/0305-4470/26/7/011

G. [. Duchi and . Schaeffer, A combinatorial approach to jumping particles, Journal of Combinatorial Theory, Series A, vol.110, issue.1, pp.1-29, 2005.
DOI : 10.1016/j.jcta.2004.09.006
URL : https://hal.archives-ouvertes.fr/hal-00019884

]. W. Fel68 and . Feller, An introduction to probability theory and its applications, 1968.

P. Flajolet, C. Puech, and J. Vuillemin, The analysis of simple list structures, Information Sciences, vol.38, issue.2, pp.121-146, 1986.
DOI : 10.1016/0020-0255(86)90016-2
URL : https://hal.archives-ouvertes.fr/inria-00076317

]. G. Lou87 and . Louchard, Random walks, Gaussian processes and list structures, Eleventh colloquium on trees in algebra and programming, pp.99-124, 1986.

J. Riordan, An introduction to combinatorial analysis, 1958.

]. T. Sas99 and . Sasamoto, One-dimensional partially asymmetric simple exclusion process with open boundaries: orthogonal polynomials approach, J. Phys. A, vol.32, issue.41, pp.7109-7131, 1999.

]. A. Shi96 and . Shiryaev, Probability, volume 95 of Graduate Texts in Mathematics, 1996.

]. R. Sim00 and . Simion, Noncrossing partitions. Discrete Math, Formal power series and algebraic combinatorics, pp.367-409, 1997.

L. [. Steingrímsson and . Williams, Permutation tableaux and permutation patterns, Journal of Combinatorial Theory, Series A, vol.114, issue.2, pp.211-234, 2007.
DOI : 10.1016/j.jcta.2006.04.001

M. Uchiyama, T. Sasamoto, and M. Wadati, Asymmetric simple exclusion process with open boundaries and Askey???Wilson polynomials, Journal of Physics A: Mathematical and General, vol.37, issue.18, pp.4985-5002, 2004.
DOI : 10.1088/0305-4470/37/18/006

]. L. Wil05 and . Williams, Enumeration of totally positive Grassmann cells, Adv. Math, vol.190, issue.2, pp.319-342, 2005.