Products of linear forms and Tutte polynomials

Let Δ be a finite sequence of n vectors from a vector space over any field. We consider the subspace of Sym ( V ) spanned by ∏ v ∈ S v , where S is a subsequence of Δ . 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 ) . Results of Ardila and Postnikov, Orlik and Terao, Terao, and Wagner are obtained as corollaries.