arXiv math/05041112005-04-06math.ACmath.CO

Linear spaces, transversal polymatroids and ASL domains

Aldo Conca

英文摘要：

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.

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