]. R. References1, J. Askey, and . Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc, vol.54, issue.319, 1985.

A. Burstein, On Some Properties of Permutation Tableaux, Annals of Combinatorics, vol.11, issue.3-4, pp.355-368, 2007.
DOI : 10.1007/s00026-007-0323-0

S. Corteel, M. Josuat-vergès, and J. S. Kim, Enumeration of type B Le-diagrams and permutation tableaux, 2011.

S. Corteel, M. Josuat-vergès, and L. K. Williams, The matrix ansatz, permutation tableaux and permutations , to appear in Adv, Appl. Math, 2012.

S. Corteel and P. Nadeau, Bijections for permutation tableaux, European Journal of Combinatorics, vol.30, issue.1, pp.295-310, 2009.
DOI : 10.1016/j.ejc.2007.12.007
URL : https://hal.archives-ouvertes.fr/hal-01185167

S. Corteel, R. Stanley, D. Stanton, and L. Williams, Formulae for Askey-Wilson moments and enumeration of staircase tableaux, Transactions of the American Mathematical Society, vol.364, issue.11, 2011.
DOI : 10.1090/S0002-9947-2012-05588-7

S. Corteel and L. Williams, Tableaux combinatorics for the asymmetric exclusion process, Advances in Applied Mathematics, vol.39, issue.3, pp.293-310, 2007.
DOI : 10.1016/j.aam.2006.08.002

S. Corteel and L. Williams, A Markov chain on permutations which projects to the asymmetric exclusion process, Int. Math. Res. Not, p.55, 2007.

S. Corteel and L. Williams, Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials, Proc. Natl. Acad. Sci. USA, pp.6726-6730, 2010.
DOI : 10.1073/pnas.0909915107

R. Koekoek, P. Lesky, and R. Swarttouw, Hypergeometric orthogonal polynomials and their qanalogues, 2010.
DOI : 10.1007/978-3-642-05014-5

T. Lam and L. K. Williams, Total positivity for cominuscule Grassmannians, New York J. Math, vol.14, pp.53-99, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01185168

P. Nadeau, The structure of alternative tableaux, Journal of Combinatorial Theory, Series A, vol.118, issue.5, pp.1638-1660, 2011.
DOI : 10.1016/j.jcta.2011.01.012

J. Novelli, J. Thibon, and L. K. Williams, Combinatorial Hopf algebras, noncommutative Hall???Littlewood functions, and permutation tableaux, Advances in Mathematics, vol.224, issue.4, pp.1311-1348, 2010.
DOI : 10.1016/j.aim.2010.01.006
URL : https://hal.archives-ouvertes.fr/hal-00823073

R. P. Stanley and E. Combinatorics, With a foreword by Gian-Carlo Rota. Corrected reprint of the 1986 original, Cambridge Studies in Advanced Mathematics, vol.1, issue.49, 1997.

E. Steingrímsson and L. 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

X. Viennot, Alternative tableaux, permutations, and partially asymmetric exclusion process, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00385528

L. Williams, Enumeration of totally positive Grassmann cells, Advances in Mathematics, vol.190, issue.2, pp.319-342, 2005.
DOI : 10.1016/j.aim.2004.01.003