Efficient generation of the ring of invariants
Journal
Journal of Algebra
Journal Volume
180
Journal Issue
2
Pages
341-363
Date Issued
1996
Author(s)
Abstract
We shall use the Binet-Minc formula in the theory of permanents to prove David Richman's theorem: Let G be a finite group acting on A := R[a1, . . . , ar], where R is any commutative ring with 1/|G|! ∈ R. Then the ring of invariants AG is generated over R by Σσ ∈ G σ(aα11aα22 ⋯ aαrr), where α1 + ⋯ + αr ≤ \G\. Applications of permanents to other problems related to invariants are given also. © 1996 Academic Press, Inc.
Type
journal article