Intersections of base rings associated to transversal polymatroids

zbMATH Open1199.13021arXiv0805.2729MaRDI QIDQ3633399

Publication date: 19 June 2009

Abstract: 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}.

Full work available at URL: https://arxiv.org/abs/0805.2729

zbMATH Keywords

Gorenstein ring canonical module polyhedral cone discrete polymatroid base ring

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Polynomial rings and ideals; rings of integer-valued polynomials (13F20)