Linear spaces, transversal polymatroids and ASL domains

Aldo Conca

paper

Linear spaces, transversal polymatroids and ASL domains

arXiv:math/0504111

Abstract

Let $K$ be an infinite field and $R = K [x_{1}, ..., x_{n}]$ be the polynomial ring. Let $V = V_{1}, ..., V_{m}$ be a collection of vector spaces of linear forms. Denote by $A (V)$ the $K$ -subalgebra of $R$ generated by the elements of the product $V_{1} ... V_{m}$ . Our goal is to investigate the properties of the algebra $A (V)$ and the relations with two problems in algebraic combinatorics White's and related conjectures on polymatroids and the study of integral posets.