论文标题
在限制整数序列的磁性磁带
On the Limiting Vacillating Tableaux for Integer Sequences
论文作者
论文摘要
分区代表理论中的基本身份为$ n^k = \sum_λf^λm_k^λ$ for $ n \ geq 2k $，其中$λ$范围均高于$ n $，$ n $，$ f^λ$的整数分区，是$ f^λ$的标准年轻$λ$ $λ$的标准年轻table $λ$，$ m__k^λ$λ$λ$，和长度$ 2K $。 Halverson和Lewandowski结合了RSK插入和Jeu de Taquin，构建了一个两次培养的$ di_n^k $，将每个整数序列映射到$ [n]^k $中的每个整数序列，以绘制由标准的年轻tableaeau和一个蒸发库组成的一对。在本文中，我们表明，对于给定的整数序列$ \ boldsymbol {i} $，当$ n $足够大时，由$ di_n^k（\ boldsymbol {i}）确定的摇摆tableaux当$ n \ rightarrow \ rightarrow \ rightarrow \ infty $;限制称为$ \ boldsymbol {i} $的限制助推图。我们给出了一组限制摇摆式tableaux的表征，并列出了列举那些摇摆不定的tableaux的明确公式。
A fundamental identity in the representation theory of the partition algeba is $n^k = \sum_λ f^λm_k^λ$ for $n \geq 2k$, where $λ$ ranges over integer partitions of $n$, $f^λ$ is the number of standard Young tableaux of shape $λ$, and $m_k^λ$ is the number of vacillating tableaux of shape $λ$ and length $2k$. Using a combination of RSK insertion and jeu de taquin, Halverson and Lewandowski constructed a bijection $DI_n^k$ that maps each integer sequence in $[n]^k$ to a pair consisting of a standard Young tableau and a vacillating tableau. In this paper, we show that for a given integer sequence $\boldsymbol{i}$, when $n$ is sufficiently large, the vacillating tableaux determined by $DI_n^k(\boldsymbol{i})$ become stable when $n \rightarrow \infty$; the limit is called the limiting vacillating tableau for $\boldsymbol{i}$. We give a characterization of the set of limiting vacillating tableaux and presents explicit formulas that enumerate those vacillating tableaux.
