Enumerative and Topological Properties of Matroids
拟阵的枚举和拓扑性质
基本信息
- 批准号:0245623
- 负责人:
- 金额:$ 7.07万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2003
- 资助国家:美国
- 起止时间:2003-07-01 至 2006-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The PI plans to continue his research into theenumerative and topological properties of matroids. Introduced in 1935 by Whitney, matroids are acombinatorial abstraction of one of the fundamentalstructures of mathematics, linear independence. Theenumerative aspect of the work involves combiningtechniques from commutative algebra, topology andcombinatorics in order to study h-vectors of brokencircuit and independence complexes. Thesecombinatorial invariants appear in applications tohyperplane arrangements, linear coding theory, networkreliability and quotients of spheres. Topologicalproperties of matroids will be explored using theinvestigator's recent discovery that matroids can berepresented as arrangements of homotopy spheres. Thispoint of view indicates possible applications tocombinatorial projective planes, oriented matroids andclassical bundle theories.This research is in the general area of combinatorics.One of the central themes in combinatorics is theenumeration of discrete objects with complicatedstructure. For instance, this proposal includesmethods for estimating the reliability of largenetworks of the type that might be found in the designof telephone or other similar communication systems.
PI计划继续他对拟阵的计数和拓扑性质的研究。拟阵是由惠特尼于1935年提出的,它是数学的基本结构之一--线性独立性的组合抽象。这项工作的计数方面涉及到结合交换代数、拓扑学和组合学的技术来研究断路和独立复形的h-向量。这些组合不变量在超平面排列、线性编码理论、网络可靠性和球面商等方面都有应用。拟阵的拓扑学性质将利用研究人员的最新发现来探索,即拟阵可以表示为同伦球面的排列。这一观点指出了组合射影平面、定向拟阵和经典丛理论的可能应用。这项研究是在组合学的一般领域。组合学的中心主题之一是具有复杂结构的离散对象的计数。例如,这项建议包括估计电话或其他类似通信系统设计中可能发现的那种大型网络可靠性的方法。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Edward Swartz其他文献
Edward Swartz的其他文献
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{{ truncateString('Edward Swartz', 18)}}的其他基金
Geometric and topological combinatorics
几何和拓扑组合学
- 批准号:
1200478 - 财政年份:2012
- 资助金额:
$ 7.07万 - 项目类别:
Continuing Grant
From Topology to Combinatorics and Back
从拓扑到组合数学并返回
- 批准号:
0900912 - 财政年份:2009
- 资助金额:
$ 7.07万 - 项目类别:
Standard Grant
f-vectors of polytopes, spheres and arrangements
多胞体、球体和排列的 f 向量
- 批准号:
0757828 - 财政年份:2008
- 资助金额:
$ 7.07万 - 项目类别:
Standard Grant
From Topology to Combinatorics and Back
从拓扑到组合数学并返回
- 批准号:
0600502 - 财政年份:2006
- 资助金额:
$ 7.07万 - 项目类别:
Continuing Grant
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