A survey of algorithms that exploit permutation symmetry to speed up computations in real algebraic geometry.
Posets for Specht ideals of essential real reflection groups
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abstract
Specht ideals are symmetric ideals in the polynomial ring generated by Specht polynomials associated with group representations. These ideals were previously studied for reflection groups of types $A$ and $B$, where their inclusion relations and their varieties reflect rich combinatorial structures. In this paper, we extend this theory to type $D$ and the dihedral groups. Our results complete the combinatorial study of Specht ideals across all infinite families of essential real reflection groups.
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Symbolic Computation with Symmetric Polynomials in Real Algebraic Geometry
A survey of algorithms that exploit permutation symmetry to speed up computations in real algebraic geometry.