arXiv subjects
Publications and source records attributed to Alin Stefan.
In this paper, the principal tool to describe transversal polymatroids with Gorenstein base ring is polyhedral geometry, especially the $Danilov-Stanley$ theorem for the characterization of canonical module. Also, we compute the $a-invariant$ and the Hilbert series of base ring associated to this class of transversal polymatroids.
In this paper we describe the facets cone associated to transversal polymatroid presented by $\mathcal{A} = \{\{1,2\},\{2,3\},...,\{n-1,n\},\{n,1\}\}.$ Using the Danilov-Stanley theorem to characterize the canonicale module, we deduce that the base ring associated to this polymatroid is Gorenstein ring. Also, starting from this polymatroid we describe the transversal polymatroids with Gorenstein base ring in dimension 3 and with the help $\it Normaliz$ in dimension 4.