. Démonstration, Les lignes du triangle eulérien avec succession d

]. D. Bibliographie-[-and81 and . André, Sur les permutations alternées, Journal de mathématiques pures et appliquées, pp.167-184

]. G. And76 and . Andrews, The theory of partitions, volume 2 of encyclopedia of mathematics and its applications, Quelques exemples de suites unimodales en théorie des nombres. Journal de théorie des nombres de Bordeaux, pp.2213-2243, 1976.

R. [. Bóna and . Ehrenborg, A combinatorial proof of the logconcavity of the numbers of permutations with k runs. arXiv preprint math, pp.20-61, 1999.

F. Bergeron, G. Labelle, and P. Leroux, Combinatorial species and tree-like structures. Number 67, 1998.
DOI : 10.1017/cbo9781107325913

]. M. Bón12 and . Bóna, Combinatorics of permutations, Unimodal, Log-concave and Pólya Frequency Sequences in Combinatorics, p.61, 1989.

L. [. Belbachir and . Szalay, Unimodal rays in the ordinary and generalized pascal triangles, Journal of Integer Sequences, vol.11, issue.107, pp.3-142, 2008.

A. [. Belbachir, C. Tebtoub, B. Carré, and . Leclerc, The 2-successive associated stirling numbers, fibonacci-stirling numbers and unimodality Splitting the square of a Schur function into its symmetric and antisymmetric parts, Comptes rendus mathématiques, pp.767-771, 1995.

L. Comtet, Advanced combinatorics, Algèbre sur un énoncé de macmahon. Comptes rendus hébdomadaire des séances de l'académie des sciences, p.561672, 1964.
DOI : 10.1007/978-94-010-2196-8

]. D. Foa97 and . Foata, Rearrangements of words. M. Lothaire, Combinatorics on Words, 1997.

]. J. Fra76 and . Françon, Arbres binaires de recherche : propriétés combinatoires et applications. Revue française d'automatique informatique recherche opérationnelle, Informatique théorique, vol.10, issue.3 5, pp.35-50, 1976.

]. F. Fro00 and . Frobenius, Über die charaktere der symmetrischen gruppe, 1900.

M. [. Foata and . Schützenberger, Théorie géométrique des polynômes eulériens, 1970.
DOI : 10.1007/BFb0060799

M. [. Foata and . Schützenberger, Nombres d'Euler et Permutations Alternantes, A survey of combinatorial theory (Proc. Internat . Sympos, pp.173-187, 1971.
DOI : 10.1016/B978-0-7204-2262-7.50021-1

D. [. Fomin and . Stanton, Rim hook lattices, St Petersburg mathematical journal of Algebra, vol.9, issue.4, pp.1007-1016, 1998.

]. W. Ful97, ]. J. Fultonfv79, G. Françon, and . Viennot, Young tableaux Permutations selon leurs pics, creux, doubles montées et double descentes, nombres d'euler et nombres de genocchi, Discrete Mathematics, vol.35, issue.281 5, pp.3121-3156, 1979.

D. [. Foata and . Zeilberger, Denert's Permutation Statistic Is Indeed Euler-Mahonian, Studies in Applied Mathematics, vol.31, issue.1, pp.31-59, 1990.
DOI : 10.1016/0012-365X(80)90173-9

]. V. Gas98 and . Gasharov, On the neggers?stanley conjecture and the eulerian polynomials Multipartite p-partitions and inner products of skew schur functions, Journal of Combinatorial Theory, Series A Contemp. Math, vol.82, issue.34 3, pp.134-146, 1984.

C. [. Gessel and . Reutenauer, Counting permutations with given cycle structure and descent set, Journal of Combinatorial Theory, Series A, vol.64, issue.2, pp.189-215, 1993.
DOI : 10.1016/0097-3165(93)90095-P

URL : https://doi.org/10.1016/0097-3165(93)90095-p

]. M. Hai89 and . Haiman, On mixed insertion, symmetry, and shifted young tableaux, Journal of Combinatorial Theory, Series A, vol.50, issue.80, pp.196-225, 1940.

F. Hivert, J. Novelli, L. Tevlin, and J. Thibon, 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

A. [. James and . Kerber, The representation theory of the symmetric group, p.25, 1981.

]. D. Knu70 and . Knuth, Permutations, matrices, and generalized young tableaux, Pacific Journal of Mathematics, vol.34, issue.3 3, pp.709-727, 1970.

]. D. Knu99, . E. Knuthlit61-]-d, ]. A. Littlewoodllt97, B. Lascoux, J. Leclerc et al., Sorting and searching On certain symmetric functions Ribbon tableaux, hall? littlewood functions, quantum affine algebras, and unipotent varieties The plactic monoid Combinatory analysis : A review of the present state of knowledge Two applications of general theorems in combinatory analysis :(1) to the theory of inversions of permutations) to the ascertainment of the numbers of terms in the development of a determinant which has amongst its elements an arbitrary number of zeros, LS81] A. Lascoux and M. P. Schützenberger. Le monoïde plaxique. Ricerca ScientMac17] P. A. MacMahon Proceedings of the London Mathematical Society, pp.426-458, 1896.

]. I. Mac95 and . Macdonald, Symmetric functions and Hall polynomials, p.79, 1995.

[. Novelli, I. Pak, and A. Stoyanovskii, A direct bijective proof of the hook-length formula, Discrete Mathematics & Theoretical Computer Science, vol.1, issue.1 10, pp.53-67, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00955690

]. B. Sag87, R. Sagan, and . Stanley, Shifted tableaux Journal of Combinatorial Theory, Series A, Sch11] I. J. Schur. Über die darstellung der symmetrischen und der alternierenden gruppe durch gebrochene lineare substitutionen. Journal für die reine und angewandte Mathematik, pp.62-103, 1911.

]. L. Ser10, . Serranosol76-]-l, and . Solomon, Longest increasing and decreasing subsequences The shifted plactic monoid A mackey formula in the group ring of a coxeter group, Canad. J. Math Mathematische Zeitschrift Journal of Algebra, vol.13, issue.462 5, pp.179-191, 1961.

B. Sagan, J. Shareshian, M. P. Wachssta89-]-r, and . Stanley, Eulerian quasisymmetric functions and cyclic sieving Log-concave and unimodal sequences in algebra , combinatorics, and geometry. Ann, Advances in Applied Mathematics New York Acad. Sci, vol.46, issue.6, pp.536-562, 1989.

]. J. Ste89 and . Stembridge, Shifted tableaux and the projective representations of symmetric groups, Advances in Mathematics, vol.74, issue.39, pp.87-134, 1989.

D. [. Stanton and . White, A schensted algorithm for rim hook tableaux, Journal of Combinatorial Theory, Series A, vol.40, issue.2, pp.211-247, 1985.
DOI : 10.1016/0097-3165(85)90088-3

M. [. Shareshian, ]. J. Wachssw10, M. Shareshian, . M. Wachstz74-]-s, M. Tanny et al., q-eulerian polynomials : excedance number and major index Electronic Research Announcements of the Eulerian quasisymmetric functions On a unimodal sequence of binomial coefficients On a unimodal sequence of binomial coefficients ii, Advances in Mathematics Discrete Mathematics Combin. Inform. System Sci, vol.13, issue.107, pp.33-45, 1974.

M. [. Tanny and . Zuker, Analytic methods applied to a sequence of binomial coefficients, Discrete Mathematics, vol.24, issue.3, pp.299-310, 1978.
DOI : 10.1016/0012-365X(78)90101-2

]. G. Vie80 and . Viennot, Une interpretation combinatoire des coefficients des développements en série entiere des fonctions elliptiques de jacobi, Journal of Combinatorial Theory, Series A, vol.29, issue.2 5, pp.121-133, 1980.

. A. Vl99-]-m and . Van-leeuwen, Edge sequences, ribbon tableaux, and an action of affine permutations, European Journal of Combinatorics, vol.20, issue.2 4, pp.179-195, 1999.

. A. Vl01-]-m and . Van-leeuwen, Some bijective correspondences involving domino tableaux, Journal of combinatorics, vol.7, issue.1, pp.35-35, 2001.

]. H. Wil, . Wilf, D. R. Generatingfunctionology, and . Worley, A theory of shifted Young tableaux On quantitative substitutional analysis, Massachusetts Institute of Technology Proceedings of the London Mathematical Society, vol.5, issue.3, pp.54-7997, 1900.