The Cones associated to some Transversal Polymatroids

zbMATH Open1206.05061arXiv0705.3954MaRDI QIDQ3605256

Alin Ştefan

Publication date: 23 February 2009

Abstract: In this paper we describe the facets cone associated to transversal polymatroid presented by $mathcalA=1,2,2,3,...,n-1,n,n,1.$ 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 $itNormaliz$ in dimension 4.

Full work available at URL: https://arxiv.org/abs/0705.3954

zbMATH Keywords

Danilov--Stanley theoremtransversal polymatroids

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Combinatorial aspects of matroids and geometric lattices (05B35) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

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