Mathematical Sciences: Research in Enumerative Combinatorics

该奖项支持Brandeis大学Ira Gessel教授在组合学方面的研究。Gessel博士计划研究对称函数和正交多项式在枚举组合学问题中的应用。其中涉及的主题包括对称函数的系数提取、排列和序列枚举、拉格朗日逆、Polya频率序列、Rook多项式、涉及正交多项式的积分的组合解释以及与Genocchi数相关的正交多项式。这项研究属于组合学的广泛范畴，这是当今数学中最活跃的领域之一。从根本上说，组合学代表着对所有数学活动中的第一项--计数--的系统化。然而，在它的现代发展中，组合数学已经不仅仅是计数，而是利用了各种各样的先进数学技术，尽管它的根源可以追溯到几个世纪前，但由于它在通信和信息技术中的重要性，该领域在过去几十年里有了爆炸性的发展。

This award supports the research in combinatorics of Professor Ira Gessel of Brandeis University. Dr. Gessel plans to study the applications of symmetric functions and orthogonal polynomials to problems in enumerative combinatorics. Among the topics involved are coefficient extraction for symmetric functions, permutation and sequence enumeration, Lagrange inversion, Polya frequency sequences, rook polynomials, combinatorial interpretations of integrals involving orthogonal polynomials, and orthogonal polynomials associated with Genocchi numbers. 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.