Molien's formula
In mathematics, Molien's formula computes the generating function attached to a linear representation of a group G on a finite-dimensional vector space, that counts the homogeneous polynomials of a given total degree that are invariants for G. It is named for Theodor Molien. Precisely, it says: given a finite-dimensional complex representation V of G and R n = C [ V ] n = Sym n ( V ∗ ) {\displaystyle R_{n}=\mathbb {C} [V]_{n}=\operatorname {Sym} ^{n}(V^{*})} , the space of homogeneous polynomial functions on V of degree n (degree-one homogeneous polynomials are precisely linear functionals), if G is a finite group, the series (called Molien series) can be computed as: ∑ n = 0 ∞ dim ( R n G ) t n = ( # G ) − 1 ∑ g ∈ G det ( 1 − t g | V ∗ ) − 1 .