Products of Linear Forms and Tutte Polynomials
Combinatorics
2010-07-29 v2
Abstract
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.
Cite
@article{arxiv.0906.4774,
title = {Products of Linear Forms and Tutte Polynomials},
author = {Andrew Berget},
journal= {arXiv preprint arXiv:0906.4774},
year = {2010}
}
Comments
Minor changes. Accepted for publication in European Journal of Combinatorics