  Let \Delta be a finite sequence of n vectors from a vector space over any
field. We consider the subspace of \operatorname{Sym}(V) spanned by \prod_{v
\in S} v, where S is a subsequence of \Delta. A result of Orlik and Terao
provides a doubly indexed direct sum of this space. The main theorem is that
the resulting Hilbert series is the Tutte polynomial evaluation
T(\Delta;1+x,y). Results of Ardila and Postnikov, Orlik and Terao, Terao, and
Wagner are obtained as corollaries.
