Mathematical Sciences: Combinatorial Theory

该奖项支持理查德教授的研究 Stanley和Gian-Carlo Rota在Combinatorics and its connections 数学的其他领域。斯坦利教授将致力于 扩展了他早期对多面体，希尔伯特函数， 对称函数，单调三角猜想，以及 微分偏序集罗塔教授将致力于不变量 理论，几何概率，本影演算，以及 物种 这项研究福尔斯属于组合学的大范畴， 这是当今数学中最活跃的领域之一。 从根本上说，组合数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，组合数学已经不仅仅是 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 of Professors Richard Stanley and Gian-Carlo Rota in Combinatorics and its connections with other areas of mathematics. Professor Stanley will work on extending his earlier research on polytopes, Hilbert functions, symmetric functions, the monotone triangle conjecture, and differential posets. Professor Rota will work on invariant theory, geometric probability, umbral calculus, and the theory of species. 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.