A class of transversal polymatroids with Gorenstein base ring
نویسنده
چکیده
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.
منابع مشابه
The Cones Associated to Some Transvesal Polymatroids
In this paper we describe the facets cone associated to transversal polymatroid presented by 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 ri...
متن کاملA ug 2 00 8 Classifications of Cohen - Macaulay modules - The base ring associated
In this thesis, we focus on the study of the base rings associated to some transversal polymatroids. A transversal polymatroid is a special kind of discrete polymatroid. Discrete polymatroids were introduced by Herzog and Hibi [16] in 2002. The thesis is structured in four chapters. Chapter 1 starts with a short excursion into convex geometry. Next, we look at some properties of affine semigrou...
متن کاملThe Cones Associated to Some Transversal Polymatroids
In this paper we describe the facets cone associated to transversal polymatroid presented by 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...
متن کاملThe Type of the Base Ring Associated to a Product of Transversal Polymatroids
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 ver...
متن کاملLinear spaces, transversal polymatroids and ASL domains
We study a class of algebras associated with linear spaces and its relations with polymatroids and integral posets, i.e. posets supporting homogeneous ASL. We prove that the base ring of a transversal polymatroid is Koszul and describe a new class of integral posets. As a corollary we obtain that every Veronese subring of a polynomial ring is an ASL.
متن کامل