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

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几类常规细胞复合体的面数来加深我们对它们的理解。 具体来说，该项目的研究将涉及使用代数、几何、拓扑和组合方法来解决涉及平衡和标记单纯复形、立方复形、单纯流形和伪流形的基本枚举问题。单元复形提供了构建各种形状的便捷方法来自更小和更简单的块，例如金字塔或立方体。一个自然的问题是：特定形状对构建块的数量有什么限制？当人们想要在计算机中表示或存储这样的结构时，这个问题的变体（例如，所需的最小块数是多少？）具有实际重要性。