Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations
作者： Hugues Verdure , Cordian Riener , Philippe Moustrou
DOI:
关键词:
摘要: An ideal of polynomials is symmetric if it closed under permutations variables. We relate general ideals to the so called Specht generated by all a given shape. show connection between leading monomials in and contained ideal. This provides applications several contexts. Most notably, this gives information about solutions corresponding set equations. From another perspective, restricts isotypic decomposition viewed as representation group.
arxiv.org
harvard.edu参考文章(27)
Ralf Fröberg, Boris Shapiro, On Vandermonde Varieties Mathematica Scandinavica. ,vol. 119, pp. 73- 91 ,(2016) , 10.7146/MATH.SCAND.A-24185
Bruce Eli Sagan, The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions ,(1991)
Grigoriy Blekherman, Cordian Riener, Symmetric nonnegative forms and sums of squares arXiv: Optimization and Control. ,(2012)
Bernard Hanzon, Dorina Jibetean, Global Minimization of a Multivariate Polynomial using Matrix Methods Journal of Global Optimization. ,vol. 27, pp. 1- 23 ,(2003) , 10.1023/A:1024664432540
Laurent Busé, Anna Karasoulou, Resultant of an equivariant polynomial system with respect to the symmetric group Journal of Symbolic Computation. ,vol. 76, pp. 142- 157 ,(2016) , 10.1016/J.JSC.2015.12.004
Jean B. Lasserre, Global Optimization with Polynomials and the Problem of Moments Siam Journal on Optimization. ,vol. 11, pp. 796- 817 ,(2000) , 10.1137/S1052623400366802
Jean-Charles Faugère, Jules Svartz, Solving polynomial systems globally invariant under an action of the symmetric group and application to the equilibria of N vortices in the plane Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12. pp. 170- 178 ,(2012) , 10.1145/2442829.2442856
Thomas Brylawski, The lattice of integer partitions Discrete Mathematics. ,vol. 6, pp. 201- 219 ,(1973) , 10.1016/0012-365X(73)90094-0
Dorina Jibetean, Monique Laurent, Semidefinite Approximations for Global Unconstrained Polynomial Optimization Siam Journal on Optimization. ,vol. 16, pp. 490- 514 ,(2005) , 10.1137/04060562X
Wilhelm Specht, Die irreduziblen Darstellungen der symmetrischen Gruppe Mathematische Zeitschrift. ,vol. 39, pp. 696- 711 ,(1935) , 10.1007/BF01201387