Mathematical Sciences: Algebraic Shifting

该奖项支持海伦·巴塞罗教授在代数组合学领域的研究。Kalai在1984年提出的代数移位法已被证明是一种非常成功的工具，可以用来表征各种简单复形的f向量。本研究的目的是探讨这种方法可能推广到代数结构，而不是简单复合体。要研究的代数结构有一个共同的性质，即它们有一类与之相关联的组合对象。这项研究属于组合学的一般领域。组合学试图找到有效的方法来研究离散的对象集合如何排列。离散系统的行为对现代通信极为重要。例如，在电话系统中出现的大网络的设计，以及计算机科学中处理离散对象集的算法的设计，这就利用了组合研究。

This award supports the research of Professor Helene Barcelo in the field of algebraic combinatorics. The algebraic shifting method introduced by Kalai in 1984 has proven to be an extremely successful tool for characterizing the f-vectors of a wide range of classes of simplicial complexes. The goal of this research is to investigate possible generalizations of this method to algebraic structures other than simplicial complexes. The algebraic structures to be studied share the common property that they have a class of combinatorial objects associated with them. This research is in the general area of Combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of lapge 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.