The type of the base ring associated to a transversal polymatroid

Details The type of the base ring associated to a transversal polymatroid The type of the base ring associated to a transversal polymatroid

2008-07-15

arxiv.org/abs/0807.2371v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

In this paper we determine the facets of the polyhedral cone generated by the exponent set of the monomials defining the base ring associated to some transversal polymatroid. We need the description of these facets to find the canonical module of the base ring which is expressed in terms of the relative interior of the cone. This would allow us to compute the $a$-invariant of those base rings. The results presented were discovered by extensive computer algebra experiments performed with {\it{Normaliz}} \cite{BK}.

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