Designs, colourings and hypergraphs

设计、着色和超图

基本信息

  • 批准号:
    217627-2010
  • 负责人:
  • 金额:
    $ 1.46万
  • 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:
    2013
  • 资助国家:
    加拿大
  • 起止时间:
    2013-01-01 至 2014-12-31
  • 项目状态:
    已结题

项目摘要

The research in this proposal is in the field of discrete mathematics known as design theory. In essence, a design having parameters N, K and L is a mathematical model in which each of N items is a member of several groups where (1) each group contains exactly K items, and (2) each pair of items are found together in exactly L of the groups. For example, if N=7, K=3 and L=1, and if the seven items of the design are represented by the letters A to G then the following seven groups produce a valid design: ABD, BCE, CDF, DEG, AEF, BFG, ACG. Designs can be used to schedule or coordinate situations in which groups with this type of structure are needed. For instance, if a farmer with seven crop varieties to plant wants to sow a mixture of three varieties in each field such that no pair of varieties is grown together in more than one field, then the example design just presented would provide a solution in which varieties A,B,D are planted in one field, B,C,E in the next field, and so forth. Sometimes the items of a design also need to be divided into collections so that no group has all K of its items coming from just one of the collections of items. For example, suppose a farmer can have one of X available treatments for disease control applied to each seed variety; varieties with a common treatment then form one collection. To reduce the risk of crop failure in each field, sowing any field with K varieties that have all had the same seed treatment is to be avoided. The design above cannot be split up into X=2 collections in this manner, but if X=3 then the three collections [A,C,E], [B,D] and [F,G] would achieve the desired result.
本提案的研究是在离散数学领域被称为设计理论。本质上,具有参数N, K和L的设计是一个数学模型,其中N个项目中的每一个都是几个组的成员,其中(1)每个组恰好包含K个项目,(2)每对项目恰好在L个组中同时出现。例如,如果N=7, K=3, L=1,并且如果设计的七个项目由字母A到G表示,则以下七个组产生有效设计:ABD, BCE, CDF, DEG, AEF, BFG, ACG。设计可以用于安排或协调需要这种类型结构的组的情况。例如,如果一个农民有七种作物品种要种植,他想在每一块地里播种三种混合品种,这样就不会有两种品种同时种植在一块地里,那么刚才展示的示例设计将提供一种解决方案,即品种a、B、D种植在一块地里,B、C、E种植在另一块地里,以此类推。有时候,设计中的道具也需要被划分成集合,这样就不会有一个组的所有K个道具都来自于其中的一个集合。例如,假设农民可以对每种种子品种采用X种可用的疾病控制方法中的一种;具有共同处理的品种然后形成一个集合。为了减少每一块地作物歉收的风险,应避免在任何一块地播种经过相同种子处理的K品种。上述设计不能以这种方式分成X=2个集合,但如果X=3,则三个集合[A,C,E], [B,D]和[F,G]将达到预期的结果。

项目成果

期刊论文数量(0)
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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, Graphs, and Networks
组合设计、图形和网络
  • 批准号:
    RGPIN-2022-03829
  • 财政年份:
    2022
  • 资助金额:
    $ 1.46万
  • 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:
    2021
  • 资助金额:
    $ 1.46万
  • 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:
    $ 1.46万
  • 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:
    $ 1.46万
  • 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:
    $ 1.46万
  • 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:
    $ 1.46万
  • 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:
    $ 1.46万
  • 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:
    $ 1.46万
  • 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:
    $ 1.46万
  • 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:
    $ 1.46万
  • 项目类别:
    Discovery Grants Program - Individual

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