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.
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