Combinatorial, Differential and Modular Partition Problems

该奖项支持弗兰克·加文在数论和组合学方面的研究。特别是，将研究三个划分问题。在最基本的层面上，划分理论处理的是计算一个数字可以被写成更小数字的和的方式的数量的问题。分拆理论与数论的其他分支，如模函数理论，有着重要的联系。它在物理学，特别是统计力学中也有重要的应用。数论的历史根源在于对整数的研究，它解决了一些问题，比如一个整数被另一个整数整除的问题。它是数学中最古老的分支之一，出于纯粹的美学原因，人们追寻了许多个世纪。然而，在过去的半个世纪里，它已经成为数据传输和处理以及通信系统等领域的各种应用中不可或缺的工具。模函数是具有高度对称性的函数。这项工作的一个主要目的是将经典的模函数理论以一种非标准的方式应用于分拆理论中的一些问题。

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.