English

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

R2 v1 2026-06-28T13:20:11.471Z