Question

英语高手进，数学论文摘要英文翻译，不要在线翻译的

论文题目：浅谈鸽笼原理的构造方法

论文摘要：鸽笼原理的运用领域非常广泛,它是组合数学中的一个最基本的原理,应用鸽笼原理可以解决许多涉及存在性的组合问题.在20世纪期间,很多研究都是针对鸽笼原理的推广,其中在Ramsey理论中达到了顶峰.正是由于鸽笼原理运用的广泛性,而针对不同类型题目的解答方法存在很大差异,因此鸽笼原理的构造方法也是多种多样.本文针对这些方法进行了整理、概括,形成了七种常用的构造方法.

关键词：鸽笼原理；构造；鸽子；笼子；分类

Answer 1

Abstracts: Principle of the use of holes for a broad range, it is a mathematical combination of the most basic principle, the application of the principle holes can solve many problems concerning the existence of a combination of issues. In the 20th century, many studies are directed at holes the promotion of the principle, Ramsey theory, in which reached its peak.It is precisely because of the extensive use of pigeon holes principle, and subject to different types of answers to very different methods, so the principle of the structure of holes is also a variety of methods. In this paper, these methods have been collated and summarized to form seven commonly used construction method.

Keywords: pigeonhole principle; structure; pigeons; cage; Category

Answer 2

The pigeon-hole principle's utilization domain is widespread, it is in a combinatorics most cardinal principle, may solve using the pigeon-hole principle many involves the existence combination question. In the 20th century period, many research are aim at the pigeon-hole principle the promotion, has achieved the crest in the Ramsey theory. Is precisely as a result of the pigeon-hole principle utilization universality, but in view of different type topic explanation method existence very big difference, therefore the pigeon-hole principle's structure method is also many and varied. This article has carried on the reorganization, the summary in view of these methods, has formed seven commonly used structure methods.