非交叉链接划分、NC（n）上的偏序<<和S-变换
Non-crossing linked partitions, the partial order << on NC(n), and the S-transform
摘要：
本文建立了自由概率中两个最近的组合发展之间的联系：Dykema在2007年引入的用于研究S-变换的非交叉链接划分，以及Belinschi和Nica在2008年引入的用于研究自由概率和布尔概率之间关系的偏序<< on NC（n）。更确切地说，在NCL（n）（{1，.，n}）和集合{（p，q）|NC（n）中的p，q，p<<q}。作为这种双射的结果，人们得到了Dykema公式的另一种描述，该公式表示非交换随机变量a的矩，表示为倒数S变换1/S_a的系数。此外，由于<<的布尔特征，该公式可以简化为类似于无c概率的矩累积量公式的形式。
英文摘要：
The paper establishes a connection between two recent combinatorial developments in free probability: the non-crossing linked partitions introduced by Dykema in 2007 to study the S-transform, and the partial order << on NC(n) introduced by Belinschi and Nica in 2008 in order to study relations between free and Boolean probability. More precisely, one has a canonical bijection between NCL(n) (the set of all non-crossing linked partitions of {1, ..., n}) and the set {(p,q) | p,q in NC(n), p<<q}. As a consequence of this bijection, one gets an alternative description of Dykema's formula expressing the moments of a noncommutative random variable a in terms of the coefficients of the reciprocal S-transform 1/S_a. Moreover, due to the Boolean features of <<, this formula can be simplified to a form which resembles the moment-cumulant formula from c-free probability.
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