Research in Combinatorics

组合学研究

• 批准号: 9704114
• 负责人: Vojtech Rodl
• 金额: $ 8.03万
• 依托单位: Emory University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704114&HistoricalAwards=false
• 关键词: Research; Combinatorics

Rodl 9704114 This award provides funds for an investigation into some research topics in three areas of discrete mathematics - Extremal Combinatorics, Ramsey Theory and Probabilistic Methods. Extremal combinatorics is an important part of combinatorial mathematics. For example a typical problem in graph theory is as follows: given a graph F determine the maximum number ex (n,F) of edges in a graph of order n not containing F. Ramsey theory investigates structures that are preserved under restricted partitions. Naturally, the classical example is the theorem of Ramsey that, in its simplest form, tells us that arbitrarily large 2-edge-colored complete graphs must contain arbitrarily large monochromatic complete subgraphs. Here the partition is given by the coloring and the structures that are preserved under this partition are the complete graphs. Probabilistic Methods have proved to be a powerful technique in combinatorics, and the theory of random graphs is a branch of graph theory that has emerged from these methods. Over the last three years, the proposer's research was mainly concentrated within these areas. The work in this project will include some problems in Ramsey theory, problems involved with possible extensions of the regularity lemma, extremal properties of random graphs, problems on delta systems and others. This research is in the area of combinatorics. One of the goals of combinatorics is to find efficient methods of studying how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research.

RODL 9704114该奖项为调查一些研究主题的研究提供了资金，该研究主题是离散数学的三个领域 - 极端组合，拉姆西理论和概率方法。极端组合学是组合数学的重要组成部分。 例如，图理论中的一个典型问题如下：给定图F确定了不包含F. ramsey理论的顺序n中的最大数字EX（n，f）。自然地，经典的示例是拉姆齐的定理，它以最简单的形式告诉我们，任意大型的2边彩色完整图必须包含任意大型单色完整子图。 在这里，分区由颜色给出，并在此分区下保存的结构是完整的图。 概率方法已被证明是组合学中的一种强大技术，随机图理论是图理论的一个分支，从这些方法中出现。 在过去的三年中，提议者的研究主要集中在这些领域。该项目中的工作将包括拉姆齐理论中的一些问题，规律性引理的可能扩展，随机图的极端特性，三角洲系统上的问题和其他问题所涉及的问题。 这项研究在组合学领域。组合主义者的目标之一是找到有效的方法来研究如何安排对象的离散收集。离散系统的行为对于现代通信非常重要。例如，大型网络的设计，例如在电话系统中发生的网络，以及计算机科学中算法的设计与离散对象集有关，这利用了组合研究。