论文标题
置换模式的稳定字符
Stable characters from permutation patterns
论文作者
论文摘要
对于固定的排列$σ\在s_k $中，令$n_σ$表示函数，将出现$σ$的出现为$ s_n $的排列模式。我们研究了$ s_n $的共轭类别的预期价值（和$ d $ thements）的$n_σ$，并证明这些类功能的不可约性角色支持稳定在$ n $增长中。这说明变量$ n，m_1，\ ldots，m_ {dk} $中有一个多项式，该矩在任何符号组的任何共轭类中计算这些瞬间（Cycle类型$ 1^{M_1} 2^{M_2} \ CDOTS \ cdots $）。该结果概括了Hultman和Gill的结果，他们证明了使用临时方法证明了$（d，k）=（1,2）$和$（1,3）$的情况。据我们所知，我们的证明是分区代数在置换模式研究中的首次应用。
For a fixed permutation $σ\in S_k$, let $N_σ$ denote the function which counts occurrences of $σ$ as a pattern in permutations from $S_n$. We study the expected value (and $d$-th moments) of $N_σ$ on conjugacy classes of $S_n$ and prove that the irreducible character support of these class functions stabilizes as $n$ grows. This says that there is a single polynomial in the variables $n, m_1, \ldots, m_{dk}$ which computes these moments on any conjugacy class (of cycle type $1^{m_1}2^{m_2}\cdots$) of any symmetric group. This result generalizes results of Hultman and of Gill, who proved the cases $(d,k)=(1,2)$ and $(1,3)$ using ad hoc methods. Our proof is, to our knowledge, the first application of partition algebras to the study of permutation patterns.
