Intersections of base rings associated to transversal polymatroids

Details Intersections of base rings associated to transversal polymatroids Intersections of base rings associated to transversal polymatroids

2008-05-18

arxiv.org/abs/0805.2729v1

Mathematics

Commutative Algebra

13 pages, 6 figures

Scientific paper

The discrete polymatroids and their base rings are studied recently in many papers (see \cite{HH}, \cite{HHV}, \cite{V1}, \cite{V2}). It is important to give conditions when the base ring associated to a transversal polymatroid is Gorenstein (see \cite{HH}). In \cite{SA} we introduced a class of such base rings. In this paper we note that an intersection of such base rings (introduced in \cite{SA}) is Gorenstein and give necessary and sufficient conditions for the intersection of two base rings from \cite{SA} to be still a base ring of a transversal polymatroid. Also, we 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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