Mathematical Sciences: Constant Term Identities and Combinatorial Enumeration

这个项目是关于常量项恒等式，组合计数，以及它们之间的相互作用。将进行四个领域的研究：常数项恒等式；多元积分及其Q-类比；某些整数数组的列举；以及常数项恒等式在证明Mills-Robbins-Rumsey猜想中的应用。这个项目涉及到使用计算机，试图解决一些问题。这些问题在组合学之外的几个领域也很有趣，如超几何级数、李理论和循环同调。

This project is about constant term identities, combinatorial enumeration, and their interaction. Four areas of research will be pursued: constant term identities; multi-variate integrals and their q-analogs; enumeration of certain arrays of integers; and uses of constant term identities in proving the Mills-Robbins-Rumsey conjectures. This project involves the use of computers in attempts to resolve some of the problems. The problems are also of interest in several areas outside of combinatorics, such as hypergeometric series, Lie theory, and cyclic homology.