论文标题
在非交通概率的组合代数
Combinatorial Hopf algebras in noncommutative probabilility
论文作者
论文摘要
我们证明，在[Arxiv：1711.00219]中引入的广泛的瞬间肿瘤关系是由Eulerian Idempotents对所罗门山脉代数的作用给出的，所罗门山脉代数的直接总和构建了单词quasi-Metressimmetric-Metressric-Metressric函数的Hopf代数$ \ wqsym $。我们证明了这些身份的$ t $ - 动物（其中$ t $的系数还给原始版本），以及戈德堡的$ t $ analogue for hausdorff系列的系数。这相当于确定所有欧拉群在指数级产品上的作用。
We prove that the generalized moment-cumulant relations introduced in [arXiv:1711.00219] are given by the action of the Eulerian idempotents on the Solomon-Tits algebras, whose direct sum builds up the Hopf algebra of Word Quasi-Symmetric Functions $\WQSym$. We prove $t$-analogues of these identities (in which the coefficient of $t$ gives back the original version), and a similar $t$-analogue of Goldberg's formula for the coefficients of the Hausdorff series. This amounts to the determination of the action of all the Eulerian idempotents on a product of exponentials.
