Combinatorial, Differential and Modular Partition Problems

9870052Garvan该奖项支持Frank Garvan在数论和组合学方面的研究。 特别是三个分区问题将被研究。 在最基本的层次上，划分理论处理的是计算一个数可以写成更小的数的和的方式的数量的问题。 划分理论与数论的其他分支如模函数理论有着重要的联系。 它也有重要的应用物理，特别是统计力学。 数论有其历史根源，在研究整个数字，解决这样的问题，如那些处理整除一个整数由另一个。 它是数学中最古老的分支之一，几个世纪以来，人们纯粹出于美学的原因而追求它。 然而，在过去的半个世纪，它已成为一个不可或缺的工具，在不同的应用领域，如数据传输和处理，通信系统。 模函数是具有高度对称性质的函数。 这项工作的一个主要目标是将经典的模函数理论以非标准的方式应用于划分理论中的一些问题。

9870052GarvanThis award supports the research of Frank Garvan in number theory and combinatorics. In particular three partition problems will be studied. At the most basic level partition theory deals with the problem of counting the number of ways a number can be written as a sum of smaller numbers. The theory of partition has had important connections with other branches of number theory such as the theory of modular functions. It has also had important applications to physics particularly statistical mechanics. Number theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems. Modular functions are functions with highly symmetric properties. One main goal of this work is to apply the classical theory of modular functions in a non-standard way to some problems in partition theory.