Efficient Generation of the Ring of Invariants Original Research Article

We shall use the Binet–Minc formula in the theory of permanents to prove David Richmanʹs theorem: LetGbe a finite group acting onAcolon, equalsR[a1,…, ar], whereRis any commutative ring with 1/G!set membership, variantR. Then the ring of invariantsAGis generated overRby ∑σset membership, variantGσ(aα11aα22···aαrr), where α1+···+αrless-than-or-equals, slantG. Applications of permanents to other problems related to invariants are given also.