Around the theory of f-vectors

摘要主要研究者：Novik， Isabella提案号：DMS - 0801152机构：华盛顿大学标题：围绕f向量理论PI将继续研究各种类型细胞复合物的面数。具体来说，她建议研究中心对称多面体、几何实现为流形的简单复合体和正集，以及立方复合体。正如先前的研究表明的那样，这将需要应用现有的和开发新的组合、代数、拓扑和可能的分析技术，从而加强数学不同部分之间的联系。细胞复合体提供了一种方便的方法，可以从更小、更简单的块构建各种形状，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施加了什么限制。当想要在计算机中表示/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。

ABSTRACTPrincipal Investigator: Novik, Isabella Proposal Number: DMS - 0801152Institution: University of WashingtonTitle: Around the theory of f-vectorsThe PI will continue studying the face numbers of various classes of cell complexes. Specifically, she proposes to work on centrally symmetric polytopes, simplicial complexes and posets whose geometric realization is a manifold, and cubical complexes. As previous works suggest, this will require applying existing and developing new combinatorial, algebraic, topological, and possibly analytical techniques, thus strengthening connections between different parts of Mathematics.Cell complexes provide a convenient way to build various shapes from smaller and simpler blocks, such as for example pyramids or cubes. A natural question then is what restrictions on the number of building blocks are imposed by specific shapes. Variations of this question (e.g., what is the minimal number of blocks required) have practical importance when one wants to represent/store such a structure in a computer.