Algebras related to matroids represented in characteristic zero
Combinatorics
2007-05-23 v2 Commutative Algebra
Rings and Algebras
Abstract
Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the structure of these algebras. In return, the numerical properties of the Hilbert function of A yield some information about the Tutte polynomial of the corresponding matroid. Isomorphism classes of these algebras correspond to equivalence classes of hyperplane arrangements under the action of the general linear group.
Cite
@article{arxiv.math/9810005,
title = {Algebras related to matroids represented in characteristic zero},
author = {David G. Wagner},
journal= {arXiv preprint arXiv:math/9810005},
year = {2007}
}
Comments
11 pages AMS-LaTeX