We reduce the conditionally monotone (c-monotone) independence of Hasebe to tensor independence on suitably constructed larger algebras. For that purpose, we use the approach developed for a reduction of similar type for boolean, free and monotone independences. We apply the tensor product realization of c-monotone random variables to introduce the c-comb (loop) product of birooted graphs, a generalization of the comb (loop) product of rooted graphs, and we show that it is related to the c-monotone additive (multiplicative) convolution of distributions.

中文翻译：

---

图的条件单调独立性和相关积

我们将 Hasebe 的条件单调（c-单调）独立性降低为在适当构造的较大代数上的张量独立性。为此，我们使用为减少布尔、自由和单调独立性的类似类型而开发的方法。我们应用c-单调随机变量的张量积实现来引入双根图的c-comb（环）积，它是有根图的梳（环）积的推广，并证明它与c-分布的单调加法（乘法）卷积。