论文标题
Plethysm系数的奥秘
The mystery of plethysm coefficients
论文作者
论文摘要
构成一般线性群的两种表示会产生Littlewood的（外部）。在字符的层面上，这提出了找到两个Schur功能的Schur扩展的问题。通常，两种Schur函数的Schur扩展系数的组合解释通常仍然是一个空旷的问题。我们确定了组合表示理论的证明技术，我们称之为“ $ s $ perp trick”，并指出了使用此想法的文献中的几个示例。我们使用$ s $ perp的技巧来提供算法来计算对称函数的单元和Schur扩展。在几种特殊情况下，这些算法比{\ sc sagemath}中当前实施的算法更有效。
Composing two representations of the general linear groups gives rise to Littlewood's (outer) plethysm. On the level of characters, this poses the question of finding the Schur expansion of the plethysm of two Schur functions. A combinatorial interpretation for the Schur expansion coefficients of the plethysm of two Schur functions is, in general, still an open problem. We identify a proof technique of combinatorial representation theory, which we call the "$s$-perp trick", and point out several examples in the literature where this idea is used. We use the $s$-perp trick to give algorithms for computing monomial and Schur expansions of symmetric functions. In several special cases, these algorithms are more efficient than those currently implemented in {\sc SageMath}.
