Convex cones and SAGBI bases of permutation invariants
  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. 
Nicolas M. Thi\'ery and St\'ephan Thomass\'e