. En, suivant la structure de l'arbre, on n'est pas sur de pouvoir énumérer tous les objets présents dans notre structure. L'exemple suivant construit de toutes les paires (i, j) dans N 2 . sage

. En-utilisant-un-parcours-en-largeur, itérateur anti-diagonal usuel. sage: breadth_search = I.breadth_first_search_iterator() sage: [breadth_search.next() for i in range(15)]

. Comme, est un espace vectoriel sur un corps cyclotomique de dimension 6! |G| = 30. On vérifie visuellement la consistance des deux neutres vis à vis du produit point par point

. Mupad-combinat and . Permutationgroupinvariantring-utilisant-les-bases-de-sagbi-gröbner, retourne exactement les mêmes invariants secondaires irréductibles. +---+ | T | MuPAD-Combinat 1.3.2 (stable) +---+---+ | A | K | an open source MuPAD package for For quick information on a particular library, please type: info(library) or ?library, | I | N | research in Algebraic Combinatorics This package provides or extends the following libraries: combinat, examples

I. Abdeljaouad, Calculs d'invariants primitifs de groupes finis, RAIRO - Theoretical Informatics and Applications, vol.33, issue.1, pp.59-77, 1999.
DOI : 10.1051/ita:1999106

URL : https://hal.archives-ouvertes.fr/hal-01148875

I. Abdeljaouad, Théorie des Invariants et Applications à la Théorie de Galois effective, 2000.

F. Bergeron, N. Borie, and N. M. Thiéry, Deformed diagonal harmonic polynomials for complex reflection groups, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00632267

F. Bergeron, Algebraic combinatorics and coinvariant spaces, CMS Treatises in Mathematics, 2009.
DOI : 10.1201/b10583

F. Bergeron, A. Garsia, and N. Wallach, Harmonics for Deformed Steenrod Operators, DMTCS proc., AN, issue.01, pp.497-508, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01186305

N. Borie and N. M. Thiéry, An evaluation approach to computing invariants rings of permutation groups, Proceedings of MEGA 2011, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00633851

A. Colin, Solving a system of algebraic equations with symmetries, Journal of Pure and Applied Algebra, vol.117, issue.118, pp.195-215, 1996.
DOI : 10.1016/S0022-4049(97)00011-X

URL : https://hal.archives-ouvertes.fr/hal-01148896

A. Colin, Théorie des invariants effective ; Applications à la théorie de Galois et à la résolution de systèmes algébriques ; Implantation en AXIOM, 1997.

H. Derksen and G. Kemper, Computational invariant theory Invariant Theory and Algebraic Transformation Groups, I, Encyclopaedia of Mathematical Sciences, 2002.
DOI : 10.1007/978-3-662-48422-7

M. D. Adderio and L. Moci, On a conjecture of Hivert and Thiéry about Steenrod operators. Arxiv preprint arXiv :1010, 2010.

X. Dahan, É. Schost, and J. Wu, Evaluation properties of invariant polynomials, Journal of Symbolic Computation, vol.44, issue.11, pp.1592-1604, 2009.
DOI : 10.1016/j.jsc.2008.12.002

S. [. Faugère and . Rahmany, Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, pp.151-158, 2009.

K. Gatermann, Symbolic solution of polynomial equation systems with symmetry, Zuse-Zentrum für Informationstechnik Berlin, 1990.

K. Geissler and J. Klüners, Galois Group Computation for Rational Polynomials, Algorithmic methods in Galois theory, pp.653-674, 2000.
DOI : 10.1006/jsco.2000.0377

URL : http://doi.org/10.1006/jsco.2000.0377

A. M. Garsia and D. Stanton, Group actions on Stanley-Reisner rings and invariants of permutation groups, Advances in Mathematics, vol.51, issue.2, pp.107-201, 1984.
DOI : 10.1016/0001-8708(84)90005-7

P. Gaudry, É. Schost, and N. M. Thiéry, EVALUATION PROPERTIES OF SYMMETRIC POLYNOMIALS, International Journal of Algebra and Computation, vol.16, issue.03, pp.505-523, 2006.
DOI : 10.1142/S0218196706003128

URL : https://hal.archives-ouvertes.fr/inria-00000629

M. Haiman, Combinatorics, symmetric functions, and Hilbert schemes In Current developments in mathematics, pp.39-111, 2002.

J. [. Hochster and . Eagon, Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci, American Journal of Mathematics, vol.93, issue.4, pp.1020-1058, 1971.
DOI : 10.2307/2373744

P. Hersh, A partitioning and related properties for the quotient complex ??(Blm)/Sl???Sm, Journal of Pure and Applied Algebra, vol.178, issue.3, pp.255-272, 2003.
DOI : 10.1016/S0022-4049(02)00192-5

F. Hivert, A. Schilling, and N. M. Thiéry, Hecke group algebras as quotients of affine Hecke algebras at level 0, Journal of Combinatorial Theory, Series A, vol.116, issue.4, pp.844-863, 2009.
DOI : 10.1016/j.jcta.2008.11.010

URL : https://hal.archives-ouvertes.fr/hal-00484687

[. Hivert and N. M. Thiéry, Deformation of symmetric functions and the rational Steenrod algebra In Invariant theory in all characteristics, of CRM Proc. Lecture Notes, pp.91-125, 2004.

[. Hivert and N. M. Thiéry, The Hecke group algebra of a Coxeter group and its representation theory, Journal of Algebra, vol.321, issue.8, pp.2230-2258, 2009.
DOI : 10.1016/j.jalgebra.2008.09.039

URL : https://hal.archives-ouvertes.fr/hal-00484684

J. E. Humphreys, Reflection groups and Coxeter groups, volume 29 of Cambridge Studies in Advanced Mathematics, 1990.

M. Kashiwara, Level zero fundamental representations over quantized affine algebras and Demazure modules, Publications of the Research Institute for Mathematical Sciences, vol.41, issue.1, pp.223-250, 2005.
DOI : 10.2977/prims/1145475409

URL : http://arxiv.org/abs/math/0309142

G. Kemper, The invar package for calculating rings of invariants, 1993.

]. S. Kin07a and . King, Minimal generating sets of non-modular invariant rings of finite groups Arxiv math/0703035, 2007.

S. A. King, Fast Computation of Secondary Invariants Arxiv math/0701270, 2007.

E. Donald and . Knuth, The art of computer programming Sorting and searching, Series in Computer Science and Information Processing, 1973.

A. Kohnert and S. Veigneau, Using Schubert Basis to Compute with Multivariate Polynomials, Advances in Applied Mathematics, vol.19, issue.1, pp.45-60, 1997.
DOI : 10.1006/aama.1997.0526

A. Lascoux, Schubert and macdonald polynomials, a parallel. preprint avaible online : www-igm. univ-mlv, 2008.

B. D. Mckay, Isomorph-Free Exhaustive Generation, Journal of Algorithms, vol.26, issue.2, pp.306-324, 1998.
DOI : 10.1006/jagm.1997.0898

C. Monico and M. D. , Counting special monomials. Recall (from, eg, Page 34 of, 2008.

V. Prosper, Factorization Properties of the q-Specialization of Schubert Polynomials, Annals of Combinatorics, vol.4, issue.1, pp.91-107, 2000.
DOI : 10.1007/PL00001278

URL : https://hal.archives-ouvertes.fr/hal-00622676

M. Pouzet and N. M. Thiéry, Invariants alg??briques de graphes et reconstruction, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.333, issue.9, pp.821-826, 2001.
DOI : 10.1016/S0764-4442(01)02137-1

URL : http://arxiv.org/abs/0812.3079

A. Ram, Affine Hecke algebras and generalized standard Young tableaux, Journal of Algebra, vol.260, issue.1, pp.367-415, 2003.
DOI : 10.1016/S0021-8693(02)00663-4

URL : http://doi.org/10.1016/s0021-8693(02)00663-4

R. C. Read, Every one a Winner or how to Avoid Isomorphism Search when Cataloguing Combinatorial Configurations, Ann. Discrete Math, vol.2, pp.107-120, 1976.
DOI : 10.1016/S0167-5060(08)70325-X

. [. Stein, The Sage Development Team, Sage Mathematics Software, 2009.

[. Seress, Permutation group algorithms, Cambridge Tracts in Mathematics, vol.152, 2003.
DOI : 10.1017/CBO9780511546549

R. P. Stanley, Invariants of finite groups and their applications to combinatorics, Bulletin of the American Mathematical Society, vol.1, issue.3, pp.475-511, 1979.
DOI : 10.1090/S0273-0979-1979-14597-X

B. Sturmfels, Algorithms in invariant theory, 1993.
DOI : 10.1007/978-3-7091-4368-1

N. M. Thiéry, Algebraic invariants of graphs; a study based on computer exploration, ACM SIGSAM Bulletin, vol.34, issue.3, pp.9-20, 2000.
DOI : 10.1145/377604.377612

N. M. Thiéry, Computing minimal generating sets of invariant rings of permutation groups with SAGBI-Gröbner basis In Discrete models : combinatorics, computation, and geometry, Discrete Math. Theor. Comput. Sci. Proc., AA, pp.315-328, 2001.

M. Nicolas, S. Thiéry, and . Thomassé, Convex cones and SAGBI bases of permutation invariants, Invariant theory in all characteristics of CRM Proc. Lecture Notes, pp.259-263, 2004.

A. Valibouze, Fonctions sym??triques et changements de bases, Lecture Notes in Comput. Sci, vol.378, pp.323-332, 1987.
DOI : 10.1007/3-540-51517-8_135

[. Veigneau, SP, a Package for Schubert Polynomials Realized with the Computer Algebra System MAPLE, Journal of Symbolic Computation, vol.23, issue.4, pp.413-425, 1997.
DOI : 10.1006/jsco.1996.0096

]. R. Woo98 and . Wood, Problems in the Steenrod algebra, Bull. London Math. Soc, vol.30, issue.5, pp.449-517, 1998.

R. M. Wood, Hit problems and the Steenrod algebra, Proceedings of the summer school Interactions between Algebraic topology and invariant theory, 2000.