Products of linear forms and Tutte polynomials

Let ΔΔ be a finite sequence of nn vectors from a vector space over any field. We consider the subspace of Sym(V)Sym(V) spanned by ∏v∈Sv∏v∈Sv, where SS is a subsequence of ΔΔ. A result of Orlik and Terao provides a doubly indexed direct sum decomposition of this space. The main theorem is that the resulting Hilbert series is the Tutte polynomial evaluation T(Δ;1+x,y)T(Δ;1+x,y). Results of Ardila and Postnikov, Orlik and Terao, Terao, and Wagner are obtained as corollaries.