où ? est la bijection décrite dans la sous-section 5.5.1, donc n + 1 ? k est l'extrémitié de la route de ? , 10. le R-mot ? ? R n,k , obtenu par ? = (? ) ?1 (T ), où ? est la bijection décrite dans la sous-section 5.5.1, donc n + 1 ? k est l'extrémité de la route de ? , 11. la suite u ? U n,k , obtenue par u = ?(?), où ? est la bijection décrite dans la sous-section 5, ?) = ?(u), où ? et ? sont les bijections décrites dans la sous-section 5.5.2, donc k est la somme des deux derniers éléments de v ,
les éléments correspondants sont décrits via les différentes bijections mentionnées dans le chapitre. De plus, dans la table, on encadre la statistique k = ? 1 si ? ? A n ,
Développement de sec x et tan x, Comptes Rendus de l'Académie des Sciences de Paris, pp.965-979, 1879. ,
Sur les permutations alternées, Journal de Mathématiques Pures et Appliquées, vol.7, issue.1881, pp.167-184 ,
A combinatorial interpretation of the Legendre-Stirling numbers, Proceedings of the, pp.2581-2590, 2009. ,
DOI : 10.1090/S0002-9939-09-09814-1
The Legendre???Stirling numbers, Discrete Mathematics, vol.311, issue.14, 2009. ,
DOI : 10.1016/j.disc.2011.02.028
Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics, Duke Mathematic Journal, vol.63, pp.537-555, 1991. ,
Combinatorics and Boson normal ordering: A gentle introduction, American Journal of Physics, vol.75, issue.7, pp.75-639, 2007. ,
DOI : 10.1119/1.2723799
URL : http://arxiv.org/abs/0704.3116
The r-Stirling numbers, Discrete Mathematics, vol.49, pp.241-259, 1984. ,
A note on downup permutations and increasing 0-1-2 trees, p.preprint, 2009. ,
Permutations with prescribed pattern, Mathematische Nachrichten, pp.5831-53, 1973. ,
Structures arborescentes, problèmes algorithmiques et combinatoires, Thèse de doctorat, 2000. ,
A combinatorial interpretation of the Seidel generation ofq-derangement numbers, Annals of Combinatorics, vol.106, issue.1, pp.313-327, 1997. ,
DOI : 10.1007/BF02558483
Alternating permutations and binary increasing trees, Journal of Combinatorial Theory Series A, vol.18, pp.141-148, 1975. ,
Interprétations combinatoires des nombres de Genocchi, Duke Mathematical Journal, vol.41, pp.305-318, 1974. ,
Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers, Advances in Applied Mathematics, vol.16, pp.275-296, 1995. ,
A Combinatorial Interpretation of the Seidel Generation of Genocchi Numbers, Annals of Discrete Mathematics, vol.6, pp.77-87, 1980. ,
DOI : 10.1016/S0167-5060(08)70696-4
Legendre-Stirling permutations, European Journal of Combinatorics, 2010. ,
Yet Another Triangle for the Genocchi Numbers, European Journal of Combinatorics, vol.21, issue.5, pp.593-600, 2000. ,
DOI : 10.1006/eujc.1999.0370
A combinatorial interpretation of the Euler and Bernoulli numbers, Nieuw Archief voor Wiskunde, vol.14, pp.241-246, 1966. ,
Legendre polynomials, Legendre???Stirling numbers, and the left-definite spectral analysis of the Legendre differential expression, Journal of Computational and Applied Mathematics, vol.148, issue.1, pp.213-238, 2002. ,
DOI : 10.1016/S0377-0427(02)00582-4
Jacobi???Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression, Journal of Computational and Applied Mathematics, vol.208, issue.1, pp.208-237, 2007. ,
DOI : 10.1016/j.cam.2006.10.045
The $q$-tangent and $q$-secant numbers via basic Eulerian polynomials, Proceedings of the American Mathematical Society, pp.385-393, 2009. ,
DOI : 10.1090/S0002-9939-09-10144-2
URL : https://hal.archives-ouvertes.fr/hal-00438479
DOUBLOONS AND NEW Q-TANGENT NUMBERS, The Quarterly Journal of Mathematics, vol.62, issue.2, p.17, 2009. ,
DOI : 10.1093/qmath/hap043
URL : https://hal.archives-ouvertes.fr/hal-00438482
Théorie géométrique des polynômes eulériens , Lecture Notes in Math no, 1970. ,
Nombres d'Euler et permutations alternantes , A survey of combinatorial theory, pp.173-187, 1973. ,
Combinatorial interpretations of the Jacobi-Stirling numbers, The Electronic Journal of Combinatorics, vol.17, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00385228
Bijections for Entringer families, European Journal of Combinatorics, vol.32, issue.1, pp.100-115, 2011. ,
DOI : 10.1016/j.ejc.2010.07.004
URL : https://hal.archives-ouvertes.fr/hal-00863456
Stirling polynomials, Journal of Combinatorial Theory, Series A, vol.24, issue.1, pp.24-33, 1978. ,
DOI : 10.1016/0097-3165(78)90042-0
URL : https://hal.archives-ouvertes.fr/hal-00843320
History of binary and other nondecimal numeration, Tomash, 1971. ,
Enumerating split-pair arrangements, Journal of Combinatorial Theory, Series A, vol.115, issue.2, pp.293-303, 2008. ,
DOI : 10.1016/j.jcta.2007.06.003
URL : http://doi.org/10.1016/j.jcta.2007.06.003
Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers, Selecta Mathematica, vol.15, issue.1, pp.105-119, 2009. ,
DOI : 10.1007/s00029-009-0489-x
URL : https://hal.archives-ouvertes.fr/hal-00484691
Combinatorics of generalized q-Euler numbers, Journal of Combinatorial Theory, Series A, vol.117, issue.4 ,
DOI : 10.1016/j.jcta.2009.07.012
A basic-sine and cosine with symbolic solutions of certain differential equations, Proceedings of Edinburgh Mathematical Society, pp.28-39, 1904. ,
Calculus of Finite Difference, 1947. ,
On the shape of polynomial curves, Tôhoku Mathematical Journal, vol.37, pp.347-362, 1933. ,
Sur les Permutations Compt??es par les Nombres de Genocchi de 1-i??re et 2-i??me Esp??ce, European Journal of Combinatorics, vol.18, issue.1, pp.18-19, 1997. ,
DOI : 10.1006/eujc.1995.0081
URL : http://doi.org/10.1006/eujc.1995.0081
Increasing trees and alternating permutations, Uspekhi Matematicheskikh Nauk. Izdatel'stvo Nauka, pp.49-79, 1994. ,
DOI : 10.1070/RM1994v049n06ABEH002448
New results on the Bochner condition about classical orthogonal polynomials, Journal of Mathematical Analysis and Applications, vol.364, issue.2, pp.307-323, 2010. ,
DOI : 10.1016/j.jmaa.2009.12.003
Combinatory Analysis, réimpression Chelsea, 1916. ,
The slopes determined by n points in the plane, Duke Mathematical Journal, vol.131, issue.1, pp.119-165, 2006. ,
Updown numbers and the initial monomials of the slope variety, Electronic Journal of Combinatorics, vol.16, issue.82, p.8, 2009. ,
De nouvelles significations énumératives des nombres d'Entringer, Discrete Mathematics, vol.38, pp.265-271, 1982. ,
Deux propriétés des arbres binaires ordonnés stricts, European Journal of Combinatorics, vol.10, pp.369-374, 1989. ,
Two other interpretations of the Entringer numbers, European Journal of Combinatorics, vol.18, pp.939-943, 1997. ,
An introduction to Combinatorial Analysis, 1958. ,
Combinatorial Identities, 1968. ,
Über eine einfache Entstehungsweise der Bernoullischen Zahlen und einiger verwandten Reihen, Sitzungsber. Münchener. Akad, vol.4, pp.157-187, 1877. ,
The <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>q</mml:mi></mml:math>-tangent and <mml:math altimg="si2.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>q</mml:mi></mml:math>-secant numbers via continued fractions, European Journal of Combinatorics, vol.31, issue.7, pp.1689-1705, 2010. ,
DOI : 10.1016/j.ejc.2010.04.003
The On-Line Encyclopedia of Integer Sequences ,
Generating functions, Studies in Combinatorics, pp.100-141, 1978. ,
A Survey of Alternating Permutations, 2009. ,
Methodus Differentialis, Sive Tractatus De Summatione et, Interpolazione Serierum Infinitorum, 1730. ,
A Sketch of his Life and Works, 1922. ,
A q-analog of the Seidel generation of Genocchi numbers, European Journal of Combinatorics, pp.27-30, 2006. ,
3)}, sur laquelle on a tracé l'équerre diagonale H 4, p.31 ,