标题： 对洗牌后循环和递增子序列结构的对称函数应用（第二部分） 显示英文标题

标题： Applications of Symmetric Functions to Cycle and Increasing Subsequence Structure after Shuffles (Part 2)

摘要： 使用Berele/Remmel/Kerov/Vershik版本的Robinson-Schensted-Knuth对应关系，我们研究了各种洗牌方法后的循环和递增子序列结构。一个结果是类似于以下的洗牌循环指标：将一副牌大致分成两等份，彻底混合第一份然后与第二份进行riffling。关于固定点的分布和循环结构的渐近分布得出了结论。给出了收敛速度的上界。与扩展的Schur函数以及Baik和Rains的工作建立了联系。 显示英文摘要

摘要： Using the Berele/Remmel/Kerov/Vershik variation of the Robinson-Schensted-Knuth correspondence, we study the cycle and increasing subsequence structure after various methods of shuffling. One consequence is a cycle index for shuffles like: cut a deck into roughly two equal piles, thoroughly mix the first pile and then riffle it with the second pile. Conclusions are drawn concerning the distribution of fixed points and the asymptotic distribution of cycle structure. An upper bound on the convergence rate is given. Connections are made with extended Schur functions and with work of Baik and Rains.