Multivariate polynomials: combinatorics and applications

多元多项式：组合数学及其应用

• 批准号: DP140102201
• 负责人: Prof Jan de Gier
• 金额: $ 23.76万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-02 至 2017-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140102201
• 关键词: Multivariate; polynomials; combinatorics; applications

Many combinatorial and computational problems in pure and applied mathematics as well as mathematical physics can be solved using polynomials in many variables. This proposal will expand our understanding of the poorly understood class of non-symmetric polynomials by studying their novel combinatorial structure. The outcomes will address the current difficulty of implementing non-symmetric polynomials in symbolic algebra packages by developing completely new computational algorithms. Secondly, this new understanding will be used to solve several challenging mathematical enumeration problems.

在纯数学和应用数学以及数学物理中的许多组合和计算问题可以使用多变量多项式来解决。这一建议将扩大我们的理解，了解不多的一类非对称多项式，通过研究其新颖的组合结构。这些成果将通过开发全新的计算算法来解决目前在符号代数包中实现非对称多项式的困难。其次，这种新的理解将被用来解决几个具有挑战性的数学枚举问题。