THE TYPE OF THE BASE RING ASSOCIATED TO A PRODUCT OF TRANSVERSAL POLYMATROIDS

Abstract

A polymatroid is a generalization of the classical notion of matroid. The main results of this paper are formulas for computing the type of base ring associated to a product of transversal polymatroids. We also present some extensive computational experiments which were needed in order to deduce the formulas. The base ring associated to a product of transversal polymatroids has multiplicity very large in general. At this moment we have examples of base rings with multiplicity of order 10^15.

Keywords

• Base ring
• transversal polymatroid
• equations of a cone
• canonical module