Mathematical Sciences: Some Problems (mostly) on Finite Sets

该奖项支持组合数学的研究， 罗格斯大学的杰弗里·卡恩教授。卡恩医生将 开展以下专题的调查： 超图（有限集的集合）; 给出了一个很好的概率估计， 一个n阶矩阵，其中所有元素都是0或1，应该是 奇异的;和Chvatal关于相交族的猜想 有限布尔代数中的理想 这项研究福尔斯属于广义的组合学范畴， 这是当今数学中最活跃的领域之一。 从根本上说，组合学代表了一个系统化的 首先是数学活动，计数在其 然而，现代的发展，组合学已经不仅仅是 计数利用各种先进的数学 技术，虽然它的根源可以追溯到几个世纪， 在过去的几十年里， 因为它在通信和信息方面的重要性， 技术.

This award supports the research in combinatorics of Professor Jeffry Kahn of Rutgers University. Dr. Kahn will be conducting investigations in the following topics: the properties of hypergraphs (collections of finite sets); the problem of giving a good estimate of the probability that a random square matrix of order n, in which all entries are zero or 1, should be singular; and Chvatal's conjecture on intersecting families in ideals in finite Boolean algebras. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.