论文标题
纬向多项式的计算和特性
Calculation and Properties of Zonal Polynomials
论文作者
论文摘要
我们研究了区域多项式，这是一个在许多数学环境中出现的对称多项式家族，例如多元统计，差异几何，表示理论和组合学。我们在Sagemath和Mathematica中介绍了两个计算机代数软件包，以进行计算。在这些软件包的帮助下，我们对区域多项式的某些特性进行了一项实验数学研究。此外，我们得出了几个无限的纬向多项式系数家族的封闭形式。
We investigate the zonal polynomials, a family of symmetric polynomials that appear in many mathematical contexts, such as multivariate statistics, differential geometry, representation theory, and combinatorics. We present two computer algebra packages, in SageMath and in Mathematica, for their computation. With the help of these software packages, we carry out an experimental mathematics study of some properties of zonal polynomials. Moreover, we derive and prove closed forms for several infinite families of zonal polynomial coefficients.
