J. Alexander and A. Hirschowitz, Polynomial interpolation in several variables, Journal of Algebraic Geometry, vol.4, issue.2, pp.201-222, 1995.

M. Ben-or and P. Tiwari, A deterministic algorithm for sparse multivariate polynomial interpolation, Proceedings of the twentieth annual ACM symposium on Theory of computing , STOC '88, 1988.
DOI : 10.1145/62212.62241

M. Bocher, The Theory of Linear Dependence, The Annals of Mathematics, vol.2, issue.1/4, pp.81-96
DOI : 10.2307/2007186

A. Borodin and P. Tiwari, On the decidability of sparse univariate polynomial interpolation, Computational Complexity, vol.27, issue.1, pp.67-90, 1991.
DOI : 10.1145/322217.322225

M. Boij, E. Carlini, and A. V. Geramita, Monomials as sums of powers: The real binary case, Proc. Amer, pp.3039-3043, 2011.
DOI : 10.1090/S0002-9939-2011-11018-9

A. Bostan, F. Chyzak, M. Giusti, R. Lebreton, G. Lecerf et al., Algorithmes efficaces en calcul formel, p.686, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01431717

M. Chiara-brambilla and G. Ottaviani, On the Alexander???Hirschowitz theorem, Journal of Pure and Applied Algebra, vol.212, issue.5, pp.1229-1251, 2008.
DOI : 10.1016/j.jpaa.2007.09.014

I. García-marco and P. Koiran, Lower bounds by Birkhoff interpolation, Journal of Complexity, vol.39
DOI : 10.1016/j.jco.2016.10.001

M. Giesbrecht, E. Kaltofen, and W. Lee, Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases, International Symposium on Symbolic and Algebraic Computation (ISSAC'2002) (Lille), pp.3-4401, 2003.
DOI : 10.1016/S0747-7171(03)00087-7

M. Giesbrecht, G. Labahn, and W. Lee, Symbolic???numeric sparse interpolation of multivariate polynomials, Journal of Symbolic Computation, vol.44, issue.8, pp.943-959, 2009.
DOI : 10.1016/j.jsc.2008.11.003
URL : http://www.cecm.sfu.ca/~pborwein/MITACS/papers/wenshin.pdf

M. Giesbrecht and D. S. Roche, Interpolation of Shifted-Lacunary Polynomials, computational complexity, vol.19, issue.3, pp.333-354, 2010.
DOI : 10.1007/s00037-010-0294-0
URL : http://arxiv.org/pdf/0810.5685

D. Grigoriev and M. Karpinski, A zero-test and an interpolation algorithm for the shifted sparse polynomials, Proc. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 10th International Symposium (AAECC-10). LNCS 673, pp.162-169, 1993.
DOI : 10.1007/3-540-56686-4_41

J. H. Grace and A. Young, The algebra of invariants, 1903.
DOI : 10.1017/CBO9780511708534

A. Iarrobino and V. Kanev, Power sums, Gorenstein algebras, and determinantal loci, Appendix C by Iarrobino and Steven L. Kleiman. Lecture Notes in Mathematics, vol.1721, 1999.
DOI : 10.1007/BFb0093426

E. Kaltofen and B. Trager, Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science, pp.301-320, 1990.
DOI : 10.1109/SFCS.1988.21946

J. Kleppe, Representing a Homogenous Polynomial as a Sum of Powers of Linear Forms Thesis for the degree of Candidatus Scientiarum, 1999.

N. Kayal, P. Koiran, T. Pecatte, and C. Saha, Lower Bounds for Sums of Powers of Low Degree Univariates, Proc. 42nd International Colloquium on Automata, Languages and Programming (ICALP 2015), part I, pp.810-821, 2015.
DOI : 10.1007/978-3-662-47672-7_66

Y. N. Lakshman and B. D. Saunders, Sparse shifts for univariate polynomials, Applicable Algebra in Engineering, Communication and Computing, vol.9, issue.3, pp.351-364, 1996.
DOI : 10.1007/3-540-56686-4_41
URL : http://www.eecis.udel.edu/~saunders/papers/sparse-interp2/aaecc.ps

M. Joseph, Z. Landsberg, and . Teitler, On the ranks and border ranks of symmetric tensors, Foundations of Computational Mathematics, vol.10, issue.3, pp.339-366, 2010.

A. K. Lenstra, H. W. Lenstra, and L. Lovász, Factoring polynomials with rational coefficients, Mathematische Annalen, vol.32, issue.4, pp.515-534, 1982.
DOI : 10.1007/BF01457454
URL : http://www.busim.ee.boun.edu.tr/~mihcak/teaching/ee684-spring07/proposed-project-papers/hard-problems/lattice-problems/lenstra.pdf

G. Pólya and G. Szegö, Problems and theorems in analysis Theory of functions , zeros, polynomials, determinants, number theory, geometry. Revised and enlarged translation by C. E. Billigheimer of the fourth German edition, 1976.

M. Voorhoeve and A. J. Van-der-poorten, Wronskian determinants and the zeros of certain functions, Indagationes Mathematicae (Proceedings), vol.78, issue.5, pp.417-424, 1975.
DOI : 10.1016/1385-7258(75)90050-5