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Convex cones and SAGBI bases of permutation invariants

Nicolas M. Thiéry·Stéphan Thomassé
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Abstract

Let G be a permutation group acting on {1,...,n}, and < be any admissible term order on the polynomial ring K[x_1,...,x_n]. We prove that the invariant ring K[x_1,...,x_n]^G of G has a finite SAGBI basis if, and only if, G is generated by reflections.

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Nicolas M. Thiéry, Stéphan Thomassé. 2006-07-17. Convex cones and SAGBI bases of permutation invariants. https://arxiv.org/abs/math/0607380

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