论文标题
评估和跨越汇合的Vandermonde形式
Evaluation and spanning sets of confluent Vandermonde forms
论文作者
论文摘要
$ n $变量中vandermonde表单的任意导数为$ [n_1 \ cdots n_n] $，其中$ i $ -th变量是区分的$ n_i-n_i-1 $ times，$ 1 \ le n_i \ le n_i \ le n-1 $。引入了一个简单的解码表以通过检查对其进行评估。 $ 0 \ le n_ {i+1} -n_i \ le 1 $ for $ 0 <i <n $的特殊情况是与功能区年轻图一对一的信件。相应的$ n！$标准色带图表地图在$ s_n $ harmonic多项式的空间中完全分级。该映射是一种有效的算法，生成了$ n！$ bases中的任何一个，带有$ n！$基础元素，均由排列索引。该结果放在多屈光波函数希尔伯特空间的几何解释的背景下。
An arbitrary derivative of a Vandermonde form in $N$ variables is given as $[n_1\cdots n_N]$, where the $i$-th variable is differentiated $N-n_i-1$ times, $1\le n_i\le N-1$. A simple decoding table is introduced to evaluate it by inspection. The special cases where $0\le n_{i+1} - n_i \le 1$ for $0<i<N$ are in one-to-one correspondence with ribbon Young diagrams. The respective $N!$ standard ribbon tableaux map to a complete graded basis in the space of $S_N$-harmonic polynomials. The mapping is realized as an efficient algorithm generating any one of $N!$ bases with $N!$ basis elements, both indexed by permutations. The result is placed in the context of a geometric interpretation of the Hilbert space of many-fermion wave functions.
