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# Symmetric Ideals, Specht Polynomials and Solutions to Symmetric Systems of Equations

arXiv: Mathematics::Commutative Algebra Mathematics::Representation Theory

[MATH]Mathematics [math], [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]

[MATH]Mathematics [math], [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]

arXiv: Mathematics::Commutative Algebra Mathematics::Representation Theory

- Université Paris Diderot France
- University of Bordeaux France
- UNIVERSITE PARIS DESCARTES France

###### 25 references, page 1 of 3

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[3] T. Brylawski. The lattice of integer partitions. Discrete mathematics, 6(3):201{219, 1973. 4 [OpenAIRE]

[4] L. Bus and A. Karasoulou. Resultant of an equivariant polynomial system with respect to the symmetric group. Journal of Symbolic Computation, 76:142 { 157, 2016. 1 [OpenAIRE]

[5] T. Church, J. S. Ellenberg, B. Farb, et al. Fi-modules and stability for representations of symmetric groups. Duke Mathematical Journal, 164(9):1833{1910, 2015. 10

[6] J.-C. Faugere and J. Svartz. Solving polynomial systems globally invariant under an action of the symmetric group and application to the equilibria of n vortices in the plane. In Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, pages 170{ 178. ACM, 2012. 1 [OpenAIRE]

[7] R. Froberg and B. Shapiro. On vandermonde varieties. Math. Scand, 119(1):7391, 2016. 4

[8] C. Goel, S. Kuhlmann, and B. Reznick. On the choi{lam analogue of hilbert's 1888 theorem for symmetric forms. Linear Algebra and its Applications, 496:114{120, 2016. 10

[9] D. Jibetean and M. Laurent. Semide nite approximations for global unconstrained polynomial optimization. SIAM Journal on Optimization, 16(2):490{514, 2005. Pagination: 25. 11 [OpenAIRE]

[10] R. Krone. Equivariant grobner bases of symmetric toric ideals. In Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, pages 311{318. ACM, 2016. 1