论文标题
通过$ n $确定因素在Vandermonde的决定因素上
On Vandermonde determinants via $n$-determinants
论文作者
论文摘要
我们使用$ n $的早期定义概念 - 决定范围范德曼德矩阵的子确定因子。首先，我们在许多特定情况下演示了我们的方法。然后，我们证明所有这些结果都可以根据Schur的多项式来说明。在我们的主要结果中，我们证明了Schur多项式等于固定基质的未成年人，该矩阵由基本对称多项式形成。这样的公式被称为第二个jaccobi-trudi身份。
We use earlier defined notion of $n$- determinant to investigate sub-determinants of an extended Vandermonde matrix. Firstly, we demonstrate our method on a number of particular cases. Then we prove that all these results may be stated in terms of Schur's polynomials. In our main result, we prove that Schur polynomials are equal to minors of a fixed matrix, which entries are formed of elementary symmetric polynomials. Such a formula is known as the second Jaccobi-Trudi identity.
