Schr\"oder trees, antipode formulas and non-commutative probability
Combinatorics
2023-11-15 v1 Probability
Rings and Algebras
Abstract
We obtain a cancellation-free formula, represented in terms of Schr\"oder trees, for the antipode in the double tensor Hopf algebra introduced by Ebrahimi-Fard and Patras. We apply the antipode formula in the context of non-commutative probability and recover cumulant-moment formulas as well as a new expression for Anshelevich's free Wick polynomials in terms of Schr\"oder trees.
Cite
@article{arxiv.2311.07824,
title = {Schr\"oder trees, antipode formulas and non-commutative probability},
author = {Adrian Celestino and Yannic Vargas},
journal= {arXiv preprint arXiv:2311.07824},
year = {2023}
}
Comments
38 pages