Calculation and Properties of Zonal Polynomials
Calculation and Properties of Zonal Polynomials
复制标题
分区多项式的计算和性质
DOI：
10.1007/s11786-020-00458-0
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发表时间：
2020
影响因子：
0.8
通讯作者：
C. Koutschan
中科院分区：
文献类型：
--
作者：
Lin Jiu;C. Koutschan
我们研究带状多项式，这是一类在许多数学领域中出现的对称多项式，例如多元统计、微分几何、表示论和组合数学。我们给出了两个计算机代数软件包，一个是在SageMath中，另一个是在Mathematica中，用于计算它们。借助这些软件包，我们对带状多项式的一些性质进行了实验数学研究。此外，我们推导并证明了几个带状多项式系数的无穷族的封闭形式。
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.