Combinatorial Designs, Graphs, and Networks

组合设计、图形和网络

基本信息

  • 批准号:
    RGPIN-2022-03829
  • 负责人:
  • 金额:
    $ 1.97万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2022
  • 资助国家:
    加拿大
  • 起止时间:
    2022-01-01 至 2023-12-31
  • 项目状态:
    已结题

项目摘要

Dr. Pike's research group tackles problems in the domains of combinatorial design theory and graph theory. Graphs are mathematical abstractions that represent the core elements of networks, namely their nodes and links between them. Graph theoretic models of networks provide a unified context in which to study diverse network problems. Problems of interest include inhibiting the spread of misinformation through social networks, and how to isolate malware in a computer network. Combinatorial designs are mathematical structures that show how to form a collection of subsets from a master set so that elements occur together a prescribed number of times among the subsets. Designs have natural applications in scheduling. For example, a type of design called a Steiner triple system can be used by a teacher who wants to assign each student to several team projects over the course of the school year so that each team has 3 students and also so that each pair of students works together in a team exactly once. Designs also have applications in coding theory and cryptography. We will study designs with strong structural properties, and which in turn correspond to scheduling scenarios with extra constraints imposed on them. We also intend to prove or refute a conjecture by Cioaba et al. that every connected strongly regular graph of even order has a Class 1 edge colouring; the remaining open case of this conjecture is for block intersection graphs of designs. One of the main goals of this proposal is to provide advanced training opportunities for students, who will acquire experience in mathematical problem solving, technical writing, and programming with parallel computing. Students will be prepared to compete in the job market and contribute to the Canadian economy.
派克博士的研究小组致力于解决组合设计理论和图论领域的问题。图是数学抽象,代表网络的核心元素,即它们的节点和它们之间的链接。网络的图论模型为研究不同的网络问题提供了统一的背景。感兴趣的问题包括抑制错误信息通过社交网络的传播,以及如何隔离计算机网络中的恶意软件。组合设计是一种数学结构,它展示了如何从主集中形成子集的集合,以便元素在子集中一起出现指定的次数。设计在调度中有天然的应用。例如,教师可以使用一种称为“斯坦纳三重系统”的设计类型,在学年中将每个学生分配到多个团队项目,以便每个团队有 3 名学生,并且每对学生在一个团队中一起工作一次。设计在编码理论和密码学中也有应用。我们将研究具有强大结构特性的设计,这些设计又对应于对其施加额外约束的调度场景。我们还打算证明或反驳 Cioaba 等人的猜想。每个偶数阶连通的强正则图都具有 1 类边着色;该猜想的剩余开放案例是针对设计的块交叉图。该提案的主要目标之一是为学生提供高级培训机会,他们将获得数学问题解决、技术写作和并行计算编程的经验。学生将准备好在就业市场竞争并为加拿大经济做出贡献。

项目成果

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Pike, David其他文献

Pike, David的其他文献

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{{ truncateString('Pike, David', 18)}}的其他基金

Combinatorial Designs and Graph Theory
组合设计和图论
  • 批准号:
    RGPIN-2016-04456
  • 财政年份:
    2021
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual
Combinatorial Designs and Graph Theory
组合设计和图论
  • 批准号:
    RGPIN-2016-04456
  • 财政年份:
    2020
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual
Combinatorial Designs and Graph Theory
组合设计和图论
  • 批准号:
    RGPIN-2016-04456
  • 财政年份:
    2019
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual
Combinatorial Designs and Graph Theory
组合设计和图论
  • 批准号:
    RGPIN-2016-04456
  • 财政年份:
    2018
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual
Combinatorial Designs and Graph Theory
组合设计和图论
  • 批准号:
    RGPIN-2016-04456
  • 财政年份:
    2017
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual
Combinatorial Designs and Graph Theory
组合设计和图论
  • 批准号:
    RGPIN-2016-04456
  • 财政年份:
    2016
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual
Designs, colourings and hypergraphs
设计、着色和超图
  • 批准号:
    217627-2010
  • 财政年份:
    2015
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual
Designs, colourings and hypergraphs
设计、着色和超图
  • 批准号:
    217627-2010
  • 财政年份:
    2014
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual
Designs, colourings and hypergraphs
设计、着色和超图
  • 批准号:
    217627-2010
  • 财政年份:
    2013
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual
Designs, colourings and hypergraphs
设计、着色和超图
  • 批准号:
    217627-2010
  • 财政年份:
    2012
  • 资助金额:
    $ 1.97万
  • 项目类别:
    Discovery Grants Program - Individual

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基于有限几何和代数方法的有限域上的设计、图形和代码的新构造
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设计、图表和代码会议
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