2020/06/03 by Franz Lehner, Lehner, Franz, Jean-Christophe Novelli +3
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2006.02089
openalex publication_date 2020/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.