Discrete Polymatroids

Reflexive polytopes and discrete polymatroids

A classification of discrete polymatroids whose independence polytopes are reflexive will be presented.

分量离散多拟阵的壳性

Shellability of Componentwise Discrete Polymatroids

本文证明了分量多拟阵理想具有线性商，从而肯定解决了Bandari和Herzog的猜想。

Classifications of Cohen-Macaulay modules - The base ring associated to a transversal polymatroid

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 \cite{HH} in 2002.

离散多面拟阵的除子类群

The divisor class group of a discrete polymatroid

本文研究离散多面拟阵的环面环，给出正规情形下除子类群与典范模类的计算方法，并对多类多面拟阵进行深入分析。

边理想的有界幂：对称交换二项式

Bounded powers of edge ideals: symmetric exchange binomials

本文研究离散多拟阵基环的toric理想生成问题，证明了几类离散多拟阵（特别是源于有限图边理想有界幂的）的toric理想可由对称交换二项式生成。

Discrete Polymatroids satisfying a stronger symmetric exchange property

In this paper we introduce discrete polymatroids satisfying the one-sided strong exchange property and show that they are sortable (as a consequence their base rings are Koszul) and that they satisfy White's conjecture. Since any pruned lattice path polymatroid satisfies the one-sided strong exchange property, this result provides an alternative proof for one of the main theorems of J. Schweig in \cite{Sc}, where it is shown that every pruned lattice path polymatroid satisfies White's conjecture. In addition, for two classes of pruned lattice path polymatroidal ideals $I$ and their powers we d…