Articles

Invariants des hypermatrices

J.-G. Luque, J.-Y. Thibon, Pfaffian and Hafnian identities in shuffle algebras, Advances in Applied Mathematics 29 (2002) 620-646.PostScript.
J.-G. Luque, J.-Y. Thibon, Hankel hyperdeterminants and Selberg integrals, J.Phys.A: Math. Gen. 36 (2003) 5267-5292 PostScript.
J.-G. Luque, J.-Y. Thibon, Hyperdeterminantal aspect of the Selberg integral, PostScript.
J.-G. Luque, Hyperdeterminants on semilattices , to appear in Linear and Multilinear Algebra, Preprint

Polynomes de Macdonald

H. Belbachir, A. Boussicault, J.-G. Luque, Hankel hyperdeterminant, rectangular Jack polynomials and even powers of the Vandermonde, Preprint
A. Boussicault, J.-G. Luque, Staircase Macdonald polynomials and the $q$-Discriminant, Preprint
J.-G. Luque, Macdonald polynomials at $t=q^k$, Preprint
J.-G. Luque, Subrectangular Macdonald polynomials and the alphabet $X^\vee$, Preprint

Théorie des invariants appliquée à l'informatique quantique

Frederic Toumazet, Jean-Gabriel Luque et Jean-Yves Thibon, Unitary invariants of qubit systems, Preprint
E. Briand, J.-G. Luque, J-Y. Thibon, A complete set of covariants of the four qubit system, J. Phys. A: Math. Gen. 36 (2003) 9915-9927. PostScript
Liste de tous les semi-invariants des 4-qubits par multidegré (format maple)
J.G. Luque et J.-Y. Thibon, Algebraic invariants of five qubits, Journal Of Physics A (submited),2005 Preprint
J.-G. Luque, J.-Y. Thibon, Polynomal invariants of four qubits, Phys. Rev. A 67, 042303 (2003) PostScript
E. Briand, J.-G. Luque, J.-Y. Thibon, F. Verstraete, The moduli space of three qutrit states, arXiv:quant-ph/0306122v2, 25 Jun 2003. PostScript
J.-G. Luque, Théorie classique des invariants et information quantique, école jeunes chercheurs 2003, université de Marne la vallée. PostScript

Algèbres de Lie libres, commutations partielles, élimination de Lazard

G. Duchamp, M. Flouret, J.G. Luque, "Théorème de Schutzenberger pour les monoïdes partiellement commutatifs libres", 2ième école AMI, Marseille 1997.
G. Duchamp, J.G. Luque, "Congruences compatible with the shuffle product", FPSAC'00, Moscow, 2000 PostScript
G. Duchamp, J.G. Luque, "Transitive factorizations", Discret.Math. special issues FPSAC'99.PostScript
G. Duchamp, E. Laugerotte, J.G. Luque, "On the support of free commutative Lie algebra", Theor. Comp. Sci. Special issues Word'99.
G. Duchamp, J.-G. Luque, Transitive Hall sets Preprint
J.-G. Luque and J.-Y. Thibon, "Noncommutative Symmetric functions associated with a code, Lazard elimination and Witt vectors",PostScript
Jean-Gabriel Luque, Jean-Christophe Novelli et Jean-Yves Thibon, Period polynomials and Ihara brackets Preprint

Automates à multiplicités

G. Duchamp, J.-G. Luque, "Lazard's Elimination (in traces) is finite state recognizable", Preprint.
G.Duchamp, M.Flouret, E.Laugerotte, J.G. Luque, "Direct and dual laws for automata with multiplicities", Theor. Comp. Sci. 267 (2001) 105-120PostScript
G. Duchamp, E. Laugerotte, J.-G. Luque, "Extending the scalar of minimizations", Proceedings, SCI 2001, Orlando PostScript

Fonctions symétriques non-commutatives

J.- G. Luque, J.-Y. Thibon, "Noncommutative symmetric functions associated with a code, Lazard elimination and Witt vectors",Preprint
G. Duchamp, J.-G. Luque, C. Tollu, "Free quasi-symmetric functions, product actions and quantum field theory of partitions",Preprint

Thèse et HDR

Monoides et Automates Admettant Un Produit de Mélange, Rouen , decembre 1999.PDF
Invariants des hypermatrices, HDR, 12 décembre 2007, PDF

Logiciels et réalisations

Une bibliothèque PSTricks-LaTex pour dessiner des polytopes complexes d'après Coxeter. Télécharger
Quelques explications sur: les polytopes en général et la blbliothèque pst-coxcoor html et la bibliothèque pst-coxeterp html

Posters

Algebraic invariants of five qubits, pdf
"Free quasi-symmetric functions, product actions and quantum field theory of partitions",pdf