等级带托空间
Hierarchical zonotopal spaces
摘要：
Zonotopal代数交织了给定线性映射X的代数、几何和组合性质。在这个理论中的基本意义是这样的事实，即代数结构是从几何中导出的（通过称为“最小映射”的非线性过程），并且代数结构的统计（例如，各种多项式理想的希尔伯特级数）是组合的，即，可使用称为“估值函数”的简单离散算法来计算。另一方面，这个理论有些僵化，因为它对给定的X只处理两对，每对都是由三个理想的嵌套序列组成的：一个外部理想（最小），一个中心理想（中间），和一个内部理想（最大）。在本文中，我们表明，zonotopal代数的基本原则，如前一段所述，通过建立一个新的组合定义zonotopal空间的整个层次，远远超出了外部，中心和内部理想的设置。
英文摘要：
Zonotopal algebra interweaves algebraic, geometric and combinatorial properties of a given linear map X. Of basic significance in this theory is the fact that the algebraic structures are derived from the geometry (via a non-linear procedure known as "the least map"), and that the statistics of the algebraic structures (e.g., the Hilbert series of various polynomial ideals) are combinatorial, i.e., computable using a simple discrete algorithm known as "the valuation function". On the other hand, the theory is somewhat rigid since it deals, for the given X, with exactly two pairs each of which is made of a nested sequence of three ideals: an external ideal (the smallest), a central ideal (the middle), and an internal ideal (the largest). In this paper we show that the fundamental principles of zonotopal algebra as described in the previous paragraph extend far beyond the setup of external, central and internal ideals by building a whole hierarchy of new combinatorially defined zonotopal spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
