Structural properties and generalizations of combinatorial designs

组合设计的结构特性和概括

基本信息

  • 批准号:
    435898-2013
  • 负责人:
  • 金额:
    $ 1.09万
  • 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:
    2015
  • 资助国家:
    加拿大
  • 起止时间:
    2015-01-01 至 2016-12-31
  • 项目状态:
    已结题

项目摘要

The origin of combinatorial designs lies in their application to the design of statistical experiments to test interactions between objects. In cases where objects are to be arranged in a circular manner, certain types of experiments can be modelled by cycle decompositions of graphs, also called cycle designs. In addition, combinatorial designs have applications to areas such as software testing, coding theory and communication systems. I propose to study structural aspects of cycle designs including colourings of the points and blocks of these designs and intersection properties of cycle designs. Colourings of the points of designs have applications in experimental design. Block colourings of designs relate to graph factorizations and the well-known Oberwolfach problem. I aim to construct certain types of cycle designs with desirable colouring properties. In addition, I will further the development of the theory of generalized designs, packings and coverings. Certain cases of these objects model various types of colourings of ordinary designs. Moreover, generalized designs, packings and coverings relate to many existing types of combinatorial designs, so their study will prove a powerful tool to combinatorial design theorists. Finally, I will consider a class of graphs called cycle intersection graphs, which are formed based on the the intersection of cycles in a cycle design. Analogues of these graphs have previously been studied for other classes of designs. One question that will be considered is whether the cycles in a design can be ordered so that consecutive cycles intersect in a particular way.
组合设计的起源在于它们应用于统计实验的设计,以测试对象之间的相互作用。在对象以圆形方式排列的情况下,某些类型的实验可以通过图的循环分解来建模,也称为循环设计。此外,组合设计在软件测试、编码理论和通信系统等领域也有应用。 我建议研究周期设计的结构方面,包括这些设计的点和块的着色和周期设计的交叉属性。 设计点的着色在实验设计中有应用。 设计的块着色与图的因子分解和著名的Oberwolfach问题有关。 我的目标是构建某些类型的周期设计与理想的着色性能。 此外,我还将进一步发展广义设计、填充和覆盖理论。这些对象的某些情况下模型的各种类型的普通设计的着色。 此外,广义设计、填充和覆盖涉及到许多现有的组合设计类型,因此它们的研究将证明是组合设计理论家的一个有力工具。 最后,我将考虑一类称为循环相交图的图,它们是基于循环设计中的循环相交而形成的。 这些图的类似物以前已经研究了其他类别的设计。 要考虑的一个问题是,设计中的循环是否可以排序,以便连续的循环以特定的方式相交。

项目成果

期刊论文数量(0)
专著数量(0)
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会议论文数量(0)
专利数量(0)

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Burgess, Andrea其他文献

Evaluation of long-acting somatostatin analog injection devices by nurses: a quantitative study
  • DOI:
    10.2147/mder.s37831
  • 发表时间:
    2012-01-01
  • 期刊:
  • 影响因子:
    1.3
  • 作者:
    Adelman, Daphne T.;Burgess, Andrea;Davies, Philippa R.
  • 通讯作者:
    Davies, Philippa R.
Hand function and self-care in children with cerebral palsy
Development of social functioning in children with cerebral palsy: A longitudinal study
Self-care and manual ability in preschool children with cerebral palsy: a longitudinal study
Development of gross motor capacity and mobility performance in children with cerebral palsy: a longitudinal study

Burgess, Andrea的其他文献

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{{ truncateString('Burgess, Andrea', 18)}}的其他基金

Designs and cycle decompositions
设计和循环分解
  • 批准号:
    RGPIN-2019-04328
  • 财政年份:
    2022
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Designs and cycle decompositions
设计和循环分解
  • 批准号:
    RGPIN-2019-04328
  • 财政年份:
    2021
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Designs and cycle decompositions
设计和循环分解
  • 批准号:
    RGPIN-2019-04328
  • 财政年份:
    2020
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Designs and cycle decompositions
设计和循环分解
  • 批准号:
    RGPIN-2019-04328
  • 财政年份:
    2019
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Structural properties and generalizations of combinatorial designs
组合设计的结构特性和概括
  • 批准号:
    435898-2013
  • 财政年份:
    2018
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Structural properties and generalizations of combinatorial designs
组合设计的结构特性和概括
  • 批准号:
    435898-2013
  • 财政年份:
    2017
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Structural properties and generalizations of combinatorial designs
组合设计的结构特性和概括
  • 批准号:
    435898-2013
  • 财政年份:
    2016
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Structural properties and generalizations of combinatorial designs
组合设计的结构特性和概括
  • 批准号:
    435898-2013
  • 财政年份:
    2014
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Structural properties and generalizations of combinatorial designs
组合设计的结构特性和概括
  • 批准号:
    435898-2013
  • 财政年份:
    2014
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual
Structural properties and generalizations of combinatorial designs
组合设计的结构特性和概括
  • 批准号:
    435898-2013
  • 财政年份:
    2013
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Discovery Grants Program - Individual

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