论文标题
迭代倍数的部分对称性
Partial symmetries of iterated plethysms
论文作者
论文摘要
这项工作强调了大型迭代的多个系数中的部分对称性的存在。所涉及的多个系数来自于迭代的成分函数的Schur扩展。 部分对称性是用分区的相互作用（翻转相关性）概括的，它概括了无处不在的$ω$相关性。具有该部分对称性的Schur阳性对称函数称为翻转对称。 如果$λ$是两个分区，则使用$s_λ$ pareSm parysm的操作。迭代的PlethySms $ s_2 \ circ s_b \ circ s_a $和$ s_c \ circ s_2 \ circ s_a $，带有$ a，$ $ $ $ b，$ b，$ b，$ b，$ $ $ $ $ 2 $的明确公式。本文以一些关于迭代多个系数的翻转对称序列的非兴趣性和渐近态性的观察，评论和开放性问题的结尾。
This work highlights the existence of partial symmetries in large families of iterated plethystic coefficients. The plethystic coefficients involved come from the expansion in the Schur basis of iterated plethysms of Schur functions indexed by one-row partitions. The partial symmetries are described in terms of an involution on partitions, the flip involution, that generalizes the ubiquitous $ω$ involution. Schur-positive symmetric functions possessing this partial symmetry are termed flip-symmetric. The operation of taking plethysm with $s_λ$ preserves flip-symmetry, provided that $λ$ is a partition of two. Explicit formulas for the iterated plethysms $s_2\circ s_b\circ s_a$ and $s_c\circ s_2\circ s_a$, with $a,$ $b,$ and $c$ $\ge$ $2$ allow us to show that these two families of iterated plethysms are flip-symmetric. The article concludes with some observations, remarks, and open questions on the unimodality and asymptotic normality of certain flip-symmetric sequences of iterated plethystic coefficients.
