Abstract :
LetRbe a commutative ring with 1, letR[X1, … ,Xn] be the polynomial ring inX1, … ,XnoverR, and letGbe an arbitrary group of permutations of {X1, … ,Xn}. This note presents a detailed analysis and a constructive combinatorial description of SAGBI bases for theR-algebra ofG-invariant polynomials. Our main result is a ground ring independent characterization of all rings of polynomial invariants of permutation groupsGhaving a finite SAGBI basis.
