Around the theory of f-vectors

围绕 f 向量理论

• 批准号: 1069298
• 负责人: Isabella Novik
• 金额: $ 21.6万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1069298&HistoricalAwards=false
• 关键词: Around; theory; vectors; Around; theory; vectors

The primary aim of this proposal is to deepen our understanding of several classes of regular cell complexes through the study of their face numbers. Specifically, research on this project will involve the use of algebraic, geometric, topological, and combinatorial methods to attack fundamental enumerative questions involving balanced and flag simplicial complexes, cubical complexes, simplicial manifolds and pseudomanifolds.Cell complexes provide a convenient way to build various shapes from smaller and simpler blocks, such as from pyramids or cubes. A natural question is: What restrictions on the number of building blocks are imposed by specific shapes? Variations of this question (e.g., What is the minimum number of blocks required?) have practical importance when one wants to represent or store such a structure in a computer.

该提案的主要目的是通过研究其面部数字来加深我们对几类常规细胞复合物的理解。 具体而言，对该项目的研究将涉及使用代数，几何，拓扑和组合方法，以攻击涉及平衡和旗帜的简单复合物，立方复合物，简单歧管和伪造的基本问题的基本枚举问题。从较小和简单的块中构建各种形状，例如，诸如simple bloves或Cubs simple blocks，或从诸如simplesers blocks，或诸如simple blocks，或者来自贵族。一个自然的问题是：特定形状对构建块的数量有什么限制？这个问题的变化（例如，需要的最小块数量是多少？）当一个人要在计算机中表示或存储这种结构时，实际上很重要。