论文标题
加权简单复合物的代数和组合特性
On algebraic and combinatorial properties of weighted simplicial complexes
论文作者
论文摘要
加权简单复合物（WSC）是描述加权节点加权云数据或网络的强大工具。在本文中，我们提出了一种通过极化概念来研究WSC的新方法。 WSC的极化使人们可以构建一种新的（未加权）的简单复合物，该复合物与称为混合花环产品的对象一致。这种新的结构保留了WSC的基础简单复合物的几种属性和不变。我们的主要重点是通过其潜在的简单络合物和混合花圈产品分析WSC。结合起来，我们研究了诸如顶点解释性，可撒性，可构造性等属性；从代数上讲，我们研究与WSC相关的理想的Betti数字，相关的素数和主要分解。
Weighted simplicial complexes (WSCs) are powerful tools for describing weighted cloud data or networks with weighted nodes. In this paper, we propose a novel approach to study WSCs via the concept of polarization. Polarization of a WSC allows one to construct a new (unweighted) simplicial complex which coincides with an object called the mixed wreath product. This new construction preserves several properties and invariants of the underlying simplicial complex of a WSC. Our main focus is to analyze WSCs through their underlying simplicial complexes and mixed wreath products. Combinatorially, we investigate properties such as vertex-decomposability, shellability, constructibility; algebraically, we study Betti numbers, associated primes and primary decompositions of ideals associated to WSCs.
