论文标题
均质和基本对称函数的3个理
3-Plethysms of homogeneous and elementary symmetric functions
论文作者
论文摘要
我们介绍了多种类型的tableaux的新组合方法，以了解出现在PlethySms中的Schur功能系数$S_ν[H_λ] $和$S_ν[E_λ] $，对于任何分区，$λ$和$ν$。我们首先给出有关这种方法的一般结果，然后在tableaux，cormbon Tableaux和多面体中使用成果，以了解$ν$是$ 3 $的分区和$λ$具有一部分的情况。然后，我们使用\ textit {kronecker map}将这些结果扩展到任何分区$λ$。
We introduce the new combinatorial approach of plethystic type of tableaux, as a method to understand coefficients of Schur functions appearing in plethysms $s_ν[h_λ]$ and $s_ν[e_λ]$, for any partitions $λ$ and $ν$. We first give general results about this approach, then use results on tableaux, ribbon tableaux and integer points in polytopes to understand the case where $ν$ is a partition of $3$ and $λ$ has one part. We then use a \textit{Kronecker map} to extend these results to any partition $λ$.
