论文标题
将同质和基本功能的正方形分为对称和反对称部分
Splitting the square of homogeneous and elementary functions into their symmetric and anti-symmetric parts
论文作者
论文摘要
我们在Schur函数的基础上考虑了完整均匀函数$h_λ$或基本对称函数$e_λ$的平方的扩展。该广场还将其分解为两个PlethySms，$ s_2 [H_λ] $和$ S_ {11} [H_λ] $（分别称为其对称性和反对称零件，分别称为其对称性和反对称零件。我们在tableaux的集合上定义了一个符号统计量，该符号索引了这些对称函数正方形中的Schur函数。该符号统计量允许确定每个Schur函数贡献哪些完整性。我们在Tableaux（Tableau和RSK上的产品）上主要使用组合工具，以及关于Plethysm和对称功能的基本操作。
We consider the expansion of the square of a complete homogeneous function $h_λ$, or of an elementary symmetric function $e_λ$, in the basis of Schur functions. This square also decomposes into two plethysms, $s_2[h_λ]$ and $s_{11}[h_λ]$ (resp. $s_2[h_λ]$ and $s_{11}[h_λ]$), which are called its symmetric and anti-symmetric parts, respectively. We define a sign statistic on the set of tableaux that index the Schur functions appearing in the square of those symmetric functions. This sign statistic allows to determine to which plethysm each Schur function contributes. We use mainly combinatorial tools on tableaux (product on tableau and RSK) and basic manipulations on plethysm and symmetric functions.
