Ramsey Theory: Central sets and related combinatorially rich sets
拉姆齐理论:中心集和相关的组合丰富集
基本信息
- 批准号:1160566
- 负责人:
- 金额:$ 21.53万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2012
- 资助国家:美国
- 起止时间:2012-07-01 至 2015-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Ramsey Theory is that part of combinatorics that deals with the question of what sort of homogeneous structures one can expect to find in some one cell of a finite partition of a specified set (or sometimes in any suitably "large" subset). For example, the simplest nontrivial instance of the infinite version of Ramsey's Theorem says that whenever the two-element subsets of the set N of positive integers are finitely colored, there must be some infinite subset of N all of whose two element subsets are the same color. Many years ago, the principal investigator proved that whenever N is finitely colored, there must exist in one color an infinite sequence together with all of its finite sums of distinct terms without repetition. The original proof was elementary, but very complicated. Subsequently, other proofs were found that were less complicated. But in 1975, F. Galvin and S. Glazer showed that this "Finite Sums Theorem" is a completely trivial consequence of the fact that the Stone-Cech compactification of N can be given an algebraic structure extending ordinary addition which makes it a compact right topological semigroup, and therefore has idempotents. Sets with the property that they contain all the finite sums from a sequence are called IP sets. By virtue of the connection discovered above, a set is an IP set if and only if it has an idempotent in its closure in the Stone-Cech compactification of N. Those that have special idempotents which are called "minimal" in their closure are "central" sets. These sets have much stronger properties, many of which are consequences of the Central Sets Theorem. But central sets have a very complicated elementary description. Sets which satisfy the conclusion of the Central Sets Theorem are called "C-sets", and are much easier to describe in an elementary fashion. The proposed investigation of these various algebraically characterized large subsets of N should continue to yield new Ramsey-theoretic results. A significant portion of the funds in this grant will provide support for graduate students at Howard University, an historically black university. In particular, the grant will provide stipends for three Ph.D. students, two of whom are black Americans, both female. This project will therefore be instrumental in training mathematicians who come from a population that is severely underrepresented within the population of US mathematicians.
拉姆齐理论是组合数学的一部分,它处理的问题是,人们可以期望在指定集合的有限分区的某个单元中找到什么样的齐次结构(有时在任何适当的“大”子集中)。 例如,拉姆齐定理的无限版本的最简单的非平凡例子说,每当正整数集合N的两个元素的子集是双着色的,必须有N的某个无限子集的两个元素的子集都是相同的颜色。 许多年前,首席研究员证明了,只要N是多色的,就一定存在一个颜色的无穷序列及其所有不同项的有限和,而不重复。 最初的证明是基本的,但非常复杂。随后,人们发现了其他不那么复杂的证明。 但在1975年,F. Galvin和S.格雷泽表明,这一“有限和定理”是一个完全平凡的后果的事实,即斯通-切赫紧化的N可以给出一个代数结构,延长普通此外,使它成为一个紧凑的权利拓扑半群,因此有幂等元。 具有包含一个序列的所有有限和的性质的集合称为IP集。 根据上面发现的联系,一个集合是IP集合当且仅当它在N的Stone-Cech紧化中的闭包中有幂等元。那些具有特殊幂等元的集合在它们的闭包中被称为“极小”的集合是“中心”集合。 这些集合具有更强的性质,其中许多是中心集合定理的结果。 但是中心集有一个非常复杂的基本描述。 满足中心集定理结论的集合被称为“C-集合”,并且更容易以初等方式描述。 建议调查这些各种代数特征的大子集N应继续产生新的拉姆齐理论的结果。这笔赠款中的很大一部分资金将为霍华德大学的研究生提供支持,这是一所历史悠久的黑人大学。 特别是,赠款将为三名博士提供津贴。学生,其中两名是美国黑人,都是女性。 因此,该项目将有助于培养来自美国数学家人口中严重代表性不足的数学家。
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)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Neil Hindman其他文献
Characterization of Simplicity and Cancellativity in βS
- DOI:
10.1007/s00233-006-0666-6 - 发表时间:
2007-05-01 - 期刊:
- 影响因子:0.700
- 作者:
Neil Hindman;Dona Strauss - 通讯作者:
Dona Strauss
On IP* sets and central sets
- DOI:
10.1007/bf01212975 - 发表时间:
1994-09-01 - 期刊:
- 影响因子:1.000
- 作者:
Vitaly Bergelson;Neil Hindman - 通讯作者:
Neil Hindman
Left large subsets of free semigroups and groups that are not right large
- DOI:
10.1007/s00233-014-9622-z - 发表时间:
2014-07-17 - 期刊:
- 影响因子:0.700
- 作者:
Neil Hindman;Lakeshia Legette Jones;Monique Agnes Peters - 通讯作者:
Monique Agnes Peters
Polynomials at iterated spectra near zero
- DOI:
10.1016/j.topol.2011.06.016 - 发表时间:
2011-09-01 - 期刊:
- 影响因子:
- 作者:
Vitaly Bergelson;Neil Hindman;Dona Strauss - 通讯作者:
Dona Strauss
Separating linear expressions in the Stone–Čech compactification of direct sums
- DOI:
10.1016/j.topol.2016.07.019 - 发表时间:
2016-11-01 - 期刊:
- 影响因子:
- 作者:
Neil Hindman;Dona Strauss - 通讯作者:
Dona Strauss
Neil Hindman的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Neil Hindman', 18)}}的其他基金
Algebra in Stone-Cech Compactifications and its Combinatorial Applications
Stone-Cech 紧化中的代数及其组合应用
- 批准号:
0852512 - 财政年份:2009
- 资助金额:
$ 21.53万 - 项目类别:
Standard Grant
Algebra in Stone-Cech Compactifications and its Combinatorial Applications
Stone-Cech 紧化中的代数及其组合应用
- 批准号:
0554803 - 财政年份:2006
- 资助金额:
$ 21.53万 - 项目类别:
Standard Grant
2003 Summer Conference on Topology and its Applications; July 9-12, 2003; Washington, DC
2003年夏季拓扑及其应用会议;
- 批准号:
0302516 - 财政年份:2003
- 资助金额:
$ 21.53万 - 项目类别:
Standard Grant
Semigroup Algebra at Infinity and its Combinatorial Applications
无穷大半群代数及其组合应用
- 批准号:
0243586 - 财政年份:2003
- 资助金额:
$ 21.53万 - 项目类别:
Continuing Grant
Semigroup Algebra at Infinity and its Combinatorial Applications
无穷大半群代数及其组合应用
- 批准号:
0070593 - 财政年份:2000
- 资助金额:
$ 21.53万 - 项目类别:
Continuing Grant
Mathematical Sciences: Ramsey Theory, The Theory of CompactLeft Topological Semigroups, and Their Interactions
数学科学:拉姆齐理论、紧左拓扑半群理论及其相互作用
- 批准号:
9424421 - 财政年份:1995
- 资助金额:
$ 21.53万 - 项目类别:
Continuing Grant
Mathematical Sciences: Combinatorics: Ultrafilters, Semigroups and Ramsey Theory
数学科学:组合数学:超滤器、半群和拉姆齐理论
- 批准号:
9025025 - 财政年份:1991
- 资助金额:
$ 21.53万 - 项目类别:
Continuing Grant
Mathematical Sciences: Combinatorics: Ultrafilters, Semigroups and Ramsey Theory
数学科学:组合数学:超滤器、半群和拉姆齐理论
- 批准号:
8901058 - 财政年份:1989
- 资助金额:
$ 21.53万 - 项目类别:
Continuing Grant
Mathematical Sciences: Ultrafilter Combinatorics: Ramsey Theory and Semigroups
数学科学:超滤组合学:拉姆齐理论和半群
- 批准号:
8520873 - 财政年份:1986
- 资助金额:
$ 21.53万 - 项目类别:
Continuing Grant
Mathematical Sciences: Ultrafilter Combinatorics: Ramsey Theory and Semigroups
数学科学:超滤组合学:拉姆齐理论和半群
- 批准号:
8320383 - 财政年份:1984
- 资助金额:
$ 21.53万 - 项目类别:
Standard Grant
相似国自然基金
Research on Quantum Field Theory without a Lagrangian Description
- 批准号:24ZR1403900
- 批准年份:2024
- 资助金额:0.0 万元
- 项目类别:省市级项目
基于isomorph theory研究尘埃等离子体物理量的微观动力学机制
- 批准号:12247163
- 批准年份:2022
- 资助金额:18.00 万元
- 项目类别:专项项目
Toward a general theory of intermittent aeolian and fluvial nonsuspended sediment transport
- 批准号:
- 批准年份:2022
- 资助金额:55 万元
- 项目类别:
英文专著《FRACTIONAL INTEGRALS AND DERIVATIVES: Theory and Applications》的翻译
- 批准号:12126512
- 批准年份:2021
- 资助金额:12.0 万元
- 项目类别:数学天元基金项目
基于Restriction-Centered Theory的自然语言模糊语义理论研究及应用
- 批准号:61671064
- 批准年份:2016
- 资助金额:65.0 万元
- 项目类别:面上项目
相似海外基金
Study of agglomeration mechanism of population based on central place theory, NEG, and population data
基于中心地理论、NEG和人口数据的人口集聚机制研究
- 批准号:
21K04299 - 财政年份:2021
- 资助金额:
$ 21.53万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Development of spatial Fourier analysis method and application to worldwide real population data for scientific verification of central place theory
空间傅里叶分析方法的发展及其在全球真实人口数据中的应用,以科学验证中心地理论
- 批准号:
18K04380 - 财政年份:2018
- 资助金额:
$ 21.53万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Study on the Development of Planning-oriented Application of Central Place Theory
中心地理论规划导向应用发展研究
- 批准号:
18K01148 - 财政年份:2018
- 资助金额:
$ 21.53万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
A Study on the Function and Prospects of Austrian Theory in Central European Cultural Studies
奥地利理论在中欧文化研究中的作用与前景研究
- 批准号:
16K02574 - 财政年份:2016
- 资助金额:
$ 21.53万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Density functional theory for molecules with non-central dipole on the basis of an anisotropic perturbation theory
基于各向异性微扰理论的非中心偶极子分子的密度泛函理论
- 批准号:
322191849 - 财政年份:2016
- 资助金额:
$ 21.53万 - 项目类别:
Research Fellowships
The study of diffusion and reception of central place theory, focusing on pioneers in central place research
中心地理论的传播与接受研究,关注中心地研究的先驱
- 批准号:
15K03017 - 财政年份:2015
- 资助金额:
$ 21.53万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Study on Regional Cooperation and Discipline of Comparative Social Pedagogy: Focusing on Theory and Practices in Central Asia
比较社会教育学区域合作与学科研究:以中亚地区理论与实践为中心
- 批准号:
15K17344 - 财政年份:2015
- 资助金额:
$ 21.53万 - 项目类别:
Grant-in-Aid for Young Scientists (B)
Ramsey Theory: Central Sets and Related Combinatorially Rich Sets
拉姆齐理论:中心集和相关组合丰富集
- 批准号:
1460023 - 财政年份:2015
- 资助金额:
$ 21.53万 - 项目类别:
Continuing Grant
Central Motivation of Depression; An Expanded Kynurenine Theory
抑郁症的核心动机;
- 批准号:
9095919 - 财政年份:2014
- 资助金额:
$ 21.53万 - 项目类别:
Central Motivation of Depression; An Expanded Kynurenine Theory
抑郁症的核心动机;
- 批准号:
9979974 - 财政年份:2014
- 资助金额:
$ 21.53万 - 项目类别: