A. D. Berenstein and A. V. Zelevinsky, Triple multiplicities for sl(r + 1) and the spectrum of the exterior algebra of the adjoint representation, Journal of Algebraic Combinatorics, vol.1, issue.1, pp.7-22, 1992.
DOI : 10.1023/A:1022429213282

S. Bravyi, Requirements for compatibility between local and multipartite quantum states, Quantum Inf. Comput, vol.4, issue.1, pp.12-26, 2004.

E. Briand, R. Orellana, and M. Rosas, Reduced Kronecker coefficients and counter? examples to Mulmuley's strong saturation conjecture SH. ArXiv:0810.3163v2, 2008.

E. Briand, R. Orellana, and M. Rosas, Quasi?polynomial formulas for the Kronecker coefficients indexed by two two?row shapes

M. Brion and M. Vergne, Residue formulae, vector partition functions and lattice points in rational polytopes, Journal of the American Mathematical Society, vol.10, issue.04, pp.797-833, 1997.
DOI : 10.1090/S0894-0347-97-00242-7

A. H. Andrew, S. Brown, M. Van-willigenburg, and . Zabrocki, Expressions for Catalan Kronecker products, 2008.

A. Buch, The saturation conjecture (after A. Knutson and T. Tao), Enseign. Math, vol.46, issue.212, pp.43-60, 2000.

P. Bürgisser and C. Ikenmeyer, The complexity of computing Kronecker coefficients, Proceedings of FPSAC 2008 (Formal Power Series and Algebraic Combinatorics), 2008.

M. Franz, Convex -a Maple package for convex geometry, version 1.1, 2006.

A. M. Garsia, G. Musiker, N. Wallach, and G. Xin, Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems, Advances in Applied Mathematics, vol.42, issue.3, pp.810-0060, 2008.
DOI : 10.1016/j.aam.2008.09.002

A. N. Kirillov, An invitation to the generalized saturation conjecture, Publications of the Research Institute for Mathematical Sciences, vol.40, issue.4, pp.1147-1239, 2004.
DOI : 10.2977/prims/1145475445

A. Klyachko, Quantum marginal problem and representations of the symmetric group. arXiv:quant-ph:0409113, 2004.

A. Knutson and T. Tao, The honeycomb model of GL n (C) tensor products. I. Proof of the saturation conjecture, Journal of the American Mathematical Society, vol.12, issue.04, pp.1055-1090, 1999.
DOI : 10.1090/S0894-0347-99-00299-4

D. E. Littlewood, Products and plethysms of characters with orthogonal, symplectic and symmetric groups, Journal canadien de math??matiques, vol.10, issue.0, pp.17-32, 1958.
DOI : 10.4153/CJM-1958-002-7

J. Luque and J. Thibon, Polynomial invariants of four qubits, Physical Review A, vol.67, issue.4, p.42303, 2003.
DOI : 10.1103/PhysRevA.67.042303

URL : https://hal.archives-ouvertes.fr/hal-00622667

D. Ketan, M. Mulmuley, and . Sohoni, Geometric complexity theory. I. An approach to the P vs. NP and related problems, SIAM J. Comput, vol.31, issue.2, pp.496-526, 2001.

D. Ketan, M. Mulmuley, and . Sohoni, Geometric complexity theory III: on deciding positivity of Littlewood?Richardson coefficients, ArXiv:cs.CC, 2005.

D. Ketan and . Mulmuley, Geometric complexity theory VI: the flip via saturated and positive integer programming in representation theory and algebraic geometry Available as arXiv:0704, 2007.

D. Ketan and . Mulmuley, Erratum to the saturation hypothesis (SH) in " Geometric Complexity Theory VI, 2008.

F. D. Murnaghan, The Analysis of the Kronecker Product of Irreducible Representations of the Symmetric Group, American Journal of Mathematics, vol.60, issue.3, pp.761-784, 1938.
DOI : 10.2307/2371610

F. D. Murnaghan, ON THE ANALYSIS OF THE KRONECKER PRODUCT OF IRREDUCIBLE REPRESENTATIONS OF Sn, Proc. Nat. Acad. Sci. U.S.A, pp.515-518, 1955.
DOI : 10.1073/pnas.41.7.515

H. Narayanan, On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients, Journal of Algebraic Combinatorics, vol.51, issue.2, pp.347-354, 2006.
DOI : 10.1007/s10801-006-0008-5

E. Rassart, A polynomiality property for Littlewood???Richardson coefficients, Journal of Combinatorial Theory, Series A, vol.107, issue.2, pp.161-179, 2004.
DOI : 10.1016/j.jcta.2004.04.003

B. Jeffrey, T. Remmel, and . Whitehead, On the Kronecker product of Schur functions of two row shapes, Bull. Belg. Math. Soc. Simon Stevin, vol.1, pp.649-683, 1994.

M. H. Rosas, The Kronecker product of Schur functions indexed by two?row shapes or hook shapes Also at arXiv:math, Journal of Algebraic Combinatorics, vol.14, issue.2, pp.153-1730001084, 2001.
DOI : 10.1023/A:1011942029902

B. Sturmfels, On vector partition functions, Journal of Combinatorial Theory, Series A, vol.72, issue.2, pp.302-309, 1995.
DOI : 10.1016/0097-3165(95)90067-5

J. Thibon, HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND TENSOR PRODUCTS OF SYMMETRIC GROUP REPRESENTATIONS, International Journal of Algebra and Computation, vol.01, issue.02, pp.207-221, 1991.
DOI : 10.1142/S0218196791000134